_{Reposting this answer to another question, because it seems relevant here as well; hopefully, this will provide the OP with a better understanding of the organic connection between the two:}

The late, great Father Thomas Hopko, former Dean of Saint Vladimir's Orthodox Theological Seminary, had the following to say, in a podcast on Ancient Faith Radio:

_{Now here we have to see a very important point for Trinitarian theology, and that is that in the Bible, in the Scriptures, and then, therefore, in the creeds—and particularly the Nicene-Constantinopolitan Creed, which became the creedal statement for ancient Christianity and remains the baptismal, liturgical creed for Eastern Orthodox churches and most Christian churches to this very day, [...] it’s very important, really critically important, to note and to affirm and to remember that the one God in whom we believe, strictly speaking, is not the Holy Trinity. The one God is God the Father. In the Bible, the one God is the Father of Jesus Christ. He is God who sends his only-begotten Son into the world, and Jesus Christ is the Son of God. Then, of course, in a parallel manner, the Spirit, the Holy Spirit, is the Spirit of God, that the Holy Spirit, being the Spirit of God, is therefore also the Spirit of Christ, the Messiah, because the Christ is the Son of God, upon whom God the Father sends and affirms his Holy Spirit.}

_{I think that this is very important, because there are wrong understandings of the Holy Trinity:}

• ^{First of all, there are those who deny that there even is a Trinity of divine Persons or divine Hypostases. They just do not understand the proper relationship between Jesus Christ, the Son of God, and God, his Father, and the Holy Spirit. So some, who might be called Unitarians or Adoptionists, or—there’s different names for them—they would say that the one God is just a uni-Personal Monad or God, and he has no Son; he does not beget; the divinity is his and his alone; and everything that exists in addition to the one God is a creature, has been created by God, has been brought into being out of nothing by God, but is certainly not an element of the very divinity and being of God himself; it doesn’t belong to God as such.}

• ^{On the other hand, there is another terrible error, and the other terrible error, usually called Modalism in technical theological terminology, is where people say there is one God who is the Holy Trinity: there is he who is the Trinity. And we Orthodox Christians, following Scripture and the creedal statements and the liturgical prayers, can never say there is one God who is the Trinity.}

_{There is one God who is the Father, and this one God who is the Father has with him eternally, whom he begets timelessly before all ages, his only-begotten Son, who is also his Logos, his Word, and also his Ḥokmot, his Sophia, his Wisdom, also his Eikona, his Icon, his Image. But this Wisdom and Word and Image and Icon of God is divine with the very same divinity as God, the one, true, and living God, because he is who he is, and he’s another who from the Father. There are three whos. There is he who is the Father, he who is the Son, and he who is the Holy Spirit. Those three whos are called the three Persons or three Hypostases.}

_{But it is important to remember that the one God is the Father of Jesus. Jesus is the Son of God. As the Nicene Creed said, “He is God from God, true God from true God.” Here the Christians would say and insist that the one God and Father, from all eternity, has with him his Son. He has with him his Son, who is of the very same divinity as he is and who was born from him, who comes forth from him, who proceeds from him; and that this one, true, and living God also has with himself his Spirit, who proceeds from him, who comes forth from him.}

_{So what we believe is that Jesus is God’s Son. Also, in St. John’s gospel, it said, “In the beginning was the Logos, and the Logos was with God and the Logos was divine.” He was in the beginning with God. All things came into being through him, and nothing came to be that is, except through him, including the very existence and life of all that exists. In him was life; in him was light. But we Orthodox Christians interpret these sentences of Scripture to show that the Logos really is divine with the same divinity as the Father. Then, in the prologue of St. John’s gospel, it says, “And the Logos became flesh, and he pitched his tent among us. He dwelt among us, full of grace and truth.” In other words, as the Nicene Creed would say:}

_{The only-begotten Son of God, begotten of the Father before all ages, Light from Light, true God from true God, begotten, not created, who for us men and for our salvation, came from heaven…}

_{Came from the realm of God. That’s what heaven means. It’s not a geographical, physical, located space. “Came down from heaven” means comes from the realm of God. “...came down from heaven and was incarnate”—sarkōthenta, became fleshed, was enfleshed, and became human. You have those two words that he became flesh and he became human. He became human. Born of the Virgin Mary, he became human. So he who was divine became human.}

_{When we say he’s truly divine, then we can call him God. St. Thomas, in the Bible, did call him God: “My Lord and my God.” The Logos is called God. Some of the sentences of St. Paul can be read as if Jesus can be called God. It depends a little bit on punctuation, but, like “Our great God and Savior, Jesus Christ”: “Our great God-and-Savior, Jesus Christ,” not “Our great God, and the Savior, Jesus Christ.” Even other Old Testament terms, like calling him Lord in a divine manner: “The Lord said to my Lord, ‘Sit at my right hand.’ ” Well, he’s using the same term for the one who sits at his right hand as for God himself, because “Lord” means “Yahweh,” and “Yahweh” is God. “Theos Kyrios”: God is the Lord; the Lord is God, and Kyrios is Yahweh in the Bible.}

_{When I was a seminarian, many years ago, I went to my professor of dogmatic theology, Professor Serge Verhovskoy, and I said to him, “Prof”—everybody called him “Prof”—“I don’t find the doctrine of the Holy Trinity in the Bible. I don’t think it’s in the Bible.” Of course, in those days, I had a very skewed idea of the Trinity. I thought of the Trinity as sort of one God who is somehow three. I thought of it as like three-leaf clovers or like three elements of water, that water could be liquid, water could be steam, and water could be ice. Actually, I came to learn that, in fact, those symbolisms are Modalistic. They’re Modalistic symbolisms; they’re not accurate. You can speak of God as fountain and stream or something like fire and heat and warmth and so on, as emanating from the one God and Father through his Son and his Spirit, but not all analogies are apt, not all are good ones, and three-leaf clovers and three forms of H2O and so on, those are not happy images, because they give the very wrong idea.}

_{Here, very interestingly, the Church Fathers of the fourth century, like Gregory the Theologian and Basil the Great and Ambrose of Milan and Hilary of Poitiers and Gregory of Nyssa, they would have never said that God the Father is of one essence with the Son. They would only say that the Son is of one essence with the Father, because the Son’s divinity is the Father’s divinity. The Son is God from God. He is a divine Person, a divine Hypostasis, from the one God.}

_{Whether we think of the one Person of the Father, who is never devoid of his Son and Spirit, whether we think of the one divinity—and here we should notice, by the way, that in Eastern Orthodoxy, the term “Triune God” is not a traditional formula. In fact, I believe you never find it in any liturgical prayer ever, the expression “Triune God.” You find the expression “Tri-Personal, tri-Hypostatic divinity,” “Theotēs” in Greek, “Bozhestvo” in Slavonic, but not “Theos” or “Bog.” There is no tri-Personal Theos, God. There is the one Theos, kai Patera, the one God and Father: “I believe in one God, the Father Almighty…” That’s the one God. But then that one God is Father eternally with his Son, who is God from God, and with his Holy Spirit.}

_{Interestingly enough, the Nicene Creed does not call the Holy Spirit “Theos, God.” Gregory the Theologian was the first one to do that, and he did it in the fourth century. St. Athanasius, when he wrote the letters to Serapion proving the divinity of the Holy Spirit, never called him “Theos,” because the Bible never calls him “Theos.” St. Basil the Great, when he wrote his treatise, On the Holy Spirit, he never called the Holy Spirit “Theos,” and Gregory the Theologian was angry with him. He said, “You’re a coward. You have to do it. The Spirit is divine with the same divinity as God the Father and the Son.” And Basil said, “Yes, he is, but let’s be careful with our language. We’re having enough trouble with the Son of God; not to get in trouble with the Holy Spirit yet.”}

_{He did call, and Nicaea did call the Son “God from God,” but it didn’t call the Spirit “God from God.” It could have, and later on, of course, it became very clear, and then, later on, the Holy Spirit is also called “Theos, God.” But we should be honest and clear and know that biblically it is never done. The closest thing in the Bible is the blasphemy of the Holy Spirit with Ananias and Sapphira, when it says they lied to God. They said, “Why did you lie to the Holy Spirit? You lied to God.” So if you lie to the Holy Spirit, you definitely lie to God the Father, whose Spirit the Holy Spirit is.}

Keeping in harmony with the ideas expressed above, I am also reposting the following explanation, from a down-voted answer to a previously asked question:

_{Let us recall that, while Adam (meaning Man) may not have been the only human in the Bible, he certainly is the only one to have borne the name of our entire species in his own person; with all of this in mind, let us now adduce the following reasoning: Just as Adam's (Man's) humanity does not infringe upon that of the beings descended from his own flesh and blood (Genesis 2:23), despite his being the only person in the entire Scripture to have ever borne the name Man as his own personal name, in virtue of his being the one father of all mankind, so also the divinity of the one God and Father does not necessarily deter other possible divine persons (personifying His various divine attributes, as Eve did with Adam's) from possibly sharing in the same divinity; notice also how the very next verse (Genesis 2:24) perfectly mirrors or resembles Christ's own idea of family unity, expressed in John 10:30.}

Posting as community wiki, since none of the ideas presented here are of my own creation.

Irenaeus was a trinitarian. The citation provided in the OP simply misunderstands Irenaeus' thoughts and words.

And through the Word Himself who had been made visible and palpable, was the Father shown forth, although all did not equally believe in Him; but all saw the Father in the Son: for the Father is the invisible of the Son, but the Son the visible of the Father. And for this reason all spake with Christ when He was present [upon earth], and they named Him God. Yea, even the demons exclaimed, on beholding the Son: “We know Thee who Thou art, the Holy One of God.” And the devil looking at Him, and tempting Him, said: “If Thou art the Son of God;”—all thus indeed seeing and speaking of the Son and the Father, but all not believing [in them]. AH IV VI 6

As well, there are other proofs of what Irenaeus truly thought.

1. Therefore neither would the Lord, nor the Holy Spirit, nor the apostles, have ever named as God, definitely and absolutely, him who was not God, unless he were truly God; nor would they have named any one in his own person Lord, except God the Father ruling over all, and His Son who has received dominion from His Father over all creation, as this passage has it: “The Lord said unto my Lord, Sit Thou at my right hand, until I make Thine enemies Thy footstool.” Here the [Scripture] represents to us the Father addressing the Son; He who gave Him the inheritance of the heathen, and subjected to Him all His enemies. Since, therefore, the Father is truly Lord, and the Son truly Lord, the Holy Spirit has fitly designated them by the title of Lord. And again, referring to the destruction of the Sodomites, the Scripture says, “Then the Lord rained upon Sodom and upon Gomorrah fire and brimstone from the Lord out of heaven.” For it here points out that the Son, who had also been talking with Abraham, had received power to judge the Sodomites for their wickedness. And this [text following] does declare the same truth: “Thy throne, O God, is for ever and ever; the sceptre of Thy kingdom is a right sceptre. Thou hast loved righteousness, and hated iniquity: therefore God, Thy God, hath anointed Thee.”3331 For the Spirit designates both [of them] by the name, of God—both Him who is anointed as Son, and Him who does anoint, that is, the Father. AH III VI 1

Irenaeus was born circa. 130 and died about 200 A.D. Athanasius lived 293 - 373 A.D. That, in itself, would explain why Irenaeus could not come under the Athanasian curses in the Creed, because Irenaeus was bone dead by the time those curses were proclaimed.

However, Irenaeus WAS a believer in the doctrine that came to be known as "the Trinity", which is the reason why he could never come under those curses. The Athanasian Creed

"...was written in Latin, probably in Gaul in the late fifth century, and was directed against the 'modalism' (similar to Sabellianism) which Priscillianism had revived in Gaul and Spain in the fourth and following centuries, and against the Arianism of the Goths and Vandals, which made the Son and the Spirit into second- and third-rank divinities." The History of Christianity p169 (Lion, 1985)

I mention this as even in the 21st century we see supporters of Modalism and Sabellianism and Arianism trying to attack those in centuries past who exposed such views. And poor old Irenaeus is a favourite target of theirs. He is much maligned and misquoted, in scraping-the-bottom-of-the-barrel efforts to denigrate the Trinity doctrine. That had been going on in John Calvin's day and he even wrote about it, to expose the twisters at work back then. Here's what Calvin said:

"27. Our adversaries falsely appeal to Irenaeus. They pile up many passages from Irenaeus [Against Heresies III vi.4] where he declares the Father of Christ to be the sole and eternal God of Israel. This is either shameful ignorance or consummate depravity. For they ought to have considered that that saintly man was dealing and contending with fanatics who denied that the Father of Christ was that same God who had of old spoken through Moses and the prophets, but fancied a sort of specter produced from the corruption of the world. Therefore he [Irenaeus] is wholly concerned with this point: to make it plain that no other God is proclaimed in Scripture than the Father of Christ, and that it is wrong to imagine another. ...In Chapter 6 of Book 3... the godly man insists on this one thing, "that he who in Scripture is called God in an absolute and undifferentiated sense is in truth the only God, and that Christ indeed is called God in an absolute sense." (Institutes of the Christian Religion Vol I, Chap XIII - In Scripture, from the creation onwards, we are taught one essence of God, which contains three Persons; ed. John T McNeill, Westminster)

Five centuries on from Calvin, the same kind of abuse against Irenaeus is seen in published partial, and cobbled quotes from Irenaeus, in an attempt to say that Trinitarians cannot claim him as a believer in the deity of Christ. I've got a booklet here that claims that "Irenaeus said that the prehuman Jesus had a separate existence from God and was inferior to him. He showed that Jesus is not equal to" God. The publishers of that booklet made no attempt to explain such quotes as Calvin brought to our attention, Irenaeus stating "that he who in Scripture is called God in an absolute and undifferentiated sense is in truth the only God, and that Christ indeed is called God in an absolute sense."

If people cherry-pick ancient literature to claim a Christian taught against what has come to be known as the Trinity doctrine, when full examination of those writings shows the opposite, then one has to wonder if they are modern-day supporters of ancient heresies those saints of yore exposed. Well, John Calvin was no slouch when it came to acquaintance with ancient literature and doctrines of the Church. It should be a lesson to us today to dig deep into Church history, to discover the hall-mark of heretical teachings that just won't lie down and die. And one trend seems to be partially quoting from, and cobbling together, bits of the old saints' writings that can be presented by them as supporting their own ideas. There's nothing new in that. Nobody should be surprised that it's gone on from shortly after the Church was established and got going, down to this very day.

You asked if Irenaeus failed to adhere to the Catholic God/Gospel, but on the matter of the deity of Christ, he adhered staunchly to the Bible God and the biblical gospel of Christ. Indeed, he is acclaimed as "The earliest theological leader of distinction in the rising church" (Williston Walker). He was a great contender against the Gnostics. In Pilgrim Theology he is listed first under the caption "Key Defenders of the Trinity in the Ancient Church". It states:

"Bishop of Lyons and student of Polycarp (who was a disciple of John the apostle). Known especially for his defense of Christianity against gnosticism (Against Heresies)." (p101, Michael Horton, Zondervan 2011)

As Irenaeus was a trinitarian (before the doctrine was finalised and put into credal form), that is why he was never 'damned'.

By its very nature, a dogma¹ makes its deniers officially heretics (ipso facto at the least) only because of its dogmatic, unequivocal nature as taught unambiguously as the faith of the Church, by unanimity of the Fathers, or a General Council, or the Pope ex cathedra.² Before something is made a dogma, it is simply be, for lack of a better word, unofficial official doctrine—the status quo of the Christian Church, to a more or less unanimous degree.

For example, before the Trintiy was dogmatized (against the hersey of Arianism), it was licit to have differing views on the precise nature of the relationship between the Father and the Son, as no teaching in any official, universal capacity was as yet made so as to be denied obstinately (and thus make heretics of its deniers). But you couldn't deny that the Son was God in general without being clearly having excised yourself by apostasy from the faith, the heart of which is the incarnation of God—Immanuel.

Paul didn't go around teaching that Jesus was h*m*ousios with the Father in the city of Jerusalem, because no one had to be taught this in order for them to accept the doctrine of the divine Son of God—not because it wasn't true: an Arius would have to come along in order for such to be later insisted upon as a necessity.

Dogmas don't work retroactively. You can't bind someone pre-Nicaea to a precise Nicene understanding of the Trinity as though they had this precise understanding available to them. Cf. John 15:22.

So no, Irenaeus, and any Pre-Nicene Father was not a heretic as incurring guilt or excommunication, but of course they could have held that opinion which is objectively heretical, which are different things.

But even according to the Pre-Nicene leniency described above, Irenaeus didn't reject the divinity of Christ (e.g.) anyway.

E.g.

Irenaeus, Against Heresies, I

The Church, though dispersed throughout the whole world, even to the ends of the earth, has received from the apostles and their disciples this faith: . . . one God, the Father Almighty, Maker of heaven, and earth, and the sea, and all things that are in them; and in one Christ Jesus, the Son of God, who became incarnate for our salvation; and in the Holy Spirit, who proclaimed through the prophets the dispensations of God, and the advents, and the birth from a virgin, and the passion, and the resurrection from the dead, and the ascension into heaven in the flesh of the beloved Christ Jesus, our Lord, and His manifestation from heaven in the glory of the Father ‘to gather all things in one,' and to raise up anew all flesh of the whole human race, in order that to Christ Jesus, our Lord, and God, and Savior, and King, according to the will of *the invisible Father, ‘every knee should bow, of things in heaven, and things in earth, and things under the earth, and that every tongue should confess; to him, and that He should execute just judgment towards all..."

Critics of the Trinity will conflate the identification of the Father as the only true God with that the Son or Holy Spirit are therefore obviously excluded from being God (since there is only one), but this ignores that a Trinitarian a) must accept that the Father is the only true God, since Scripture states it, and more importantly to the fallaciousness of this objection 2) believe the Son and the Holy Ghost ontologically owe their origin and nature to the Father, the only true God—this is what makes them God. The Trinity is in fact a lot closer to Modalism than anything else, since the distinction of the Persons is one that is not of nature, meaning all three Persons are equally eternal and equally have proper to them the ineffable, unique, and only divine nature: the onotological order of 'Father,' 'Son,' and 'Holy Ghost' are only ones of opposition of relation, not of order of coming into being—as soon as there is a Divine Nature, it is the Father, the Son and the Holy Ghost. The Father is the Divine Nature. The Son is the Divine Nature. The Holy Ghost is the Divine Nature. They are ineffably distinct in this way, but not as to their Nature—to be יהוה. They are the same God, but not the same person.

This is why the Trinitarin Creed doesn't say 'We believe in one God, the Father, and one God, the Son, and one God, etc.' But "We believe in one God, the Father, Maker of all things visible and invisible. .... and in one Lord Jesus Christ, the Only-begotten Son of God... etc.' only later to declare the divinity that flows from this Sonship of necessity and by its very nature.

This is perhaps synonymous with the objection that 'the Son is not God, He is the Son of God.' But this is a strawman of the Trinity if used as an objection thereto. This is because the Son is only called God because He shares one and the exact same nature with the Father, not because He is the Father (is 'God' in that Unitarian sense). That is 'Son of God' and 'God' are synonymous precisely because the Son is God by virtue of His nature being that of the Father, not because 'the Father' and 'the Son' refer to the same person. They do not: the Father, or the Son, or the Holy Ghost refer to the same God. Any time when the Father is called 'the only true God' it speaks of the fact that the Son and the Holy Ghost are ontologically distinct from this their [ontological] Origin, which can as being such be spoken of as 'the only' of its kind.

^{1 As used as a technical term, the word dogma means a doctrine declared by the Church in such a capacity as to bind all believers to its acceptance (usually/almost without exception in contradistinction to heretical versions of the doctrine, or its denial). It doesn't mean that before it enoyed this necessity of belief it was not true, or not believed.}

^{2 The objective infalliblity of the doctrine in such instances simply means that since Christ promised His Church will not be overcome by the gates of Hell, not overthrowing of the faith will happen—which would have happened if a doctrine was taught in these respective capacities by necessity (e.g. the Pope binding the Church to a specific understanding of Scripture/doctrine would require all to believe it, hence it must, if Christ's Church really never will fail absolutely, be true and dogmatically so).}