Good for you! This is exactly what you're supposed to do, and I don't know why so many people have a problem doing these three things, when they've been told they've caused emotional harm to another. It's embarrassing to do ot, and it doesn't feel good, but you're right. Your feelings are not the most important in this moment.

1. Acknowledge the harm you caused.
2. Apologize for the harm you caused.
3. Don't do it again.