Wasn't Peter just trying to avoid getting caught when he denied Jesus three times?

One might argue that a "two-fold" sin occurred; one of pride (Peter's boasting) and one of fear (failure to trust God).

John was present at the chief priest's house and did not deny his discipleship, but still lived to witness the crucifixion. But Peter essentially lied with an oath (which Jesus had strictly forbidden, Matt 5:34-36), "Again he denied it with an oath. 'I do not know the man,' he said." (Matt 26:72) for fear of finding himself on a fourth cross next to Jesus. That was not God's plan for Peter (at least, not for many more years), but Peter was so overwhelmed by fear that he abandoned Christ to his face.

While we can understand the betrayal of Judas, seeing that he was close to Jesus in proximity only (but neither in heart or spirit), Peter was one of the "inner circle", making his "in your face" betrayal much harder to excuse.

Frankly, we EXPECT our enemies or those who don't know us well to turn on us when adversity threatens their well being. But the betrayal of one in whom we have placed trust and confidence? I would have to strongly disagree with your initial assessment that, "...it wasn't that bad."

Reading related passages helps to understand Scripture; the sin was pride.

Peter's denying Jesus is set up by something that happened previous to that infamous denial during Jesus' night time interrogation. From the book of Matthew (26: 31-35):

31 Then Jesus said to them, "This night all of you will have your faith in me shaken, for it is written: 'I will strike the shepherd, and the sheep of the flock will be dispersed'; 32 but after I have been raised up, I shall go before you to Galilee." 33 Peter said to him in reply, "Though all may have their faith in you shaken, mine will never be." 34 Jesus said to him, "Amen, I say to you, this very night before the c**k crows, you will deny me three times." 35 Peter said to him, "Even though I should have to die with you, I will not deny you." And all the disciples spoke likewise.

Peter talked a good game. He boasted of his faith and love for Jesus. And when it came to crunch time, he could not back up his words.
(Matthew, 26: 72-75)

72 Again he denied it with an oath, "I do not know the man!" 73 A little later the bystanders came over and said to Peter, "Surely you too are one of them; even your speech gives you away." 74 At that he began to curse and to swear, "I do not know the man." And immediately a c**k crowed. 75 Then Peter remembered the word that Jesus had spoken: "Before the c**k crows you will deny me three times." He went out and began to weep bitterly.

Peter's sin was the sin of pride, as evidenced by his boasting to Jesus and the other disciples present.

Whether or not it was "some great sin" to react with fear, Peter's boast demonstrates the hazards of pride, and the other matter of walking the walk versus talking the talk. While I've generally heard it taught (by clergy in various denominations) that this was a case of Peter's faith being put to the test -- as any of us can be presented with a test of faith -- there are many lessons to learn from this.

Pride goeth before a fall ¹

One lesson is: don't write checks with your words that your faith can't cash.

Lesson two: don't boast

As the Apostle Paul cautions us: don't be boastful. Peter was boasting about how strong his faith was when he'd no idea what test his faith was about to be presented with. Jesus knew.
1 Corinthians 1: 27-31

27 Rather, God chose the foolish of the world to shame the wise, and God chose the weak of the world to shame the strong, 28 and God chose the lowly and despised of the world, those who count for nothing, to reduce to nothing those who are something, 29 so that no human being might boast before God. 30 It is due to him that you are in Christ Jesus, who became for us wisdom from God, as well as righteousness, sanctification, and redemption, 31 so that, as it is written, "Whoever boasts, should boast in the Lord."

Peter was boasting in Peter, not the Lord, and so had a fall.

¹ A slight misquote of Proverbs 16:18

Pride goeth before destruction, and an haughty spirit before a fall