Yes, what your boyfriend did was absolutely inappropriate. Yes, being drunk isn’t an excuse. But since you say he acknowledged what happened and apologized and, especially, since you said that he is a kind and loving guy, it’s just possible that this was a horrible mistake that won’t be repeated.
That doesn’t make it okay. Non-consensual sex is never okay. But his responsible reaction to your reaction may make it possible for the two of you to work things out together and move on. He has learned a hard lesson in what can happen when someone is as disinhibited as he was when that drunk.
It would help you feel better if the two of you talk about how much alcohol he can and can’t handle and make some rules around it. I suspect he already knows that If he continues to drink to that level of impairment, the consequences to your relationship will be dire. But it will help you trust him again if he acknowledges that self-awareness and agrees to ground rules around his drinking.
Forgiveness isn’t something someone can earn. It is a gift we give a person we think is worth it. Trust grows and remains when the other continues to treat our trust with respect and care.
Only you can decide if you can forgive his mistake and trust your boyfriend to not let it happen again. In this case, I do encourage you to look at everything you know about him, not just the very bad decision he made one night.
I wish you well.