There is a lot of advice out there that tells men to be strong with women, and always be dominant. But this can go too far. And with the more confident (and better) women, it won't be put up with for long.
None of us are perfect. In a relationship there will always be times when you are wrong. When this happens, and you know you are in the wrong. Own up to it and apologize.
Here's how to apologize for something: Own up to what you did. Look her in the eye and say you're sorry (or "I was a jerk" or "I was an idiot" or whatever). Don't spend time explaining why you did it, or what your intentions were, or why what you did wasn't really all that bad.
If she continues to talk about it. Add this: "Look, I'm sorry. I apologize. I was being an idiot. It won't happen again. What more can I do to make you feel better about it now?".
Focus on her emotional state, not her logical processes. And don't dwell on the subject. It's not good for either of you or the relationship. Make each other feel better (good emotional state) and move on.