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In suttas Buddha says this to people feeling remorseful about their past: there is no use worrying about the past you can't change. Focus on acting with skill going forward.
One of the most underappreciated techniques in Buddhism is weaving useful narratives. This is when you tell yourself a story about yourself in a way that induces and sustains the good states of mind. The story can't be a lie though! -- so before you can do it, you have to actually repent/reconcile/resolve to not let it happen again.
So the first step is to actually finalize the internal decision: what shall you do differently from now on. Then you should let some time pass to give you a chance to act in the new way. And then you can say hey, I have not committed the same mistake for such and such time, I think I am good now. Simple, right?
Check out the story about Angulimala and a Pregnant Woman. It illustrates this principle brilliantly.
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You have to practice maitreyi (loving-kindness) towards yourself. It's much easier for us to forgive others than it is for us to forgive ourselves. However, it's very important that we show loving kindness towards ourselves as well.
You should determine to not to make that mistake again. Regret is one of the five hindrances which prevents you from achieving nirvana, so practice loving kindness towards yourself and let go of the regret.
Look up the story of Angulimala. The following books by Ajahn Brahm are brilliant as well: Mindfulness, Bliss, and Beyond: A Meditator's Handbook, Opening the Door of Your Heart.