You can give specific apologies for your behavior without having to explain specifically why. In fact it may even be better to say "I take full responsibility for x, y and z and I'm sorry".

I have a friend who does horrible, terrible appalling things on a regular basis. She is actually notorious in the small city where I live because once she starts drinking she has literally no impulse control and says whatever offensive thing pops into her head.

She is also an all-star champion at apologies. Probably because she has to do it all the time. She is sincere and she doesn't make excuses. They are usually along the lines of "I really messed up, I understand how that affected you, nothing about that was okay, I am so sorry" and she genuinely means it.

Sometimes she also gives incredibly thoughtful little gifts that show just how well she knows what you love most.