Does this "feel bad" seems to mean "regret or feel guilty"?, but many times "feel bad" seems to mean "upset or angry". Does the meaning change a lot?
W: What's wrong with Sujin? Boy, she looks really upset.
M :Actually, it's because of me. I made fun of her in front of the class.
W:Why did you do that ?
M : I didn't know it would hurt her feelings. I feel bad about my mistake.
W: Now that you know, you'd better go to her and tell her that you're sorry.
"To feel bad" can have several meanings and the context will tell you which one. You're right that in this context, it means that he feels guilty about what he did to Sujin.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.