Hey Homer,
I don't think it's a crime to go out with friends 2 days in a row. And sometimes that may include a bit of a hang over. I don't think you did something wrong, necessarily, depending on how you treated your friend.
If you were unable to do what was planned or were snippy. I think I'd be looking to apologize for whatever behavior or consequence hurt your friend, and not the hangover itself. The hangover is a little bit of an excuse for the behavior and not the behavior itself. So for example, my mom may do something that is hurtful and instead of saying "I am so sorry I hurt you in x,y,z way. That must have made you feel _____." She'll say "well I'm sorry! I'm trying my best! I was under a lot of stress!" So the apology is about the excuse and not my feelings.
I've also learned in therapy something of a formula for communication called 5 secrets of effective communication and what I like about it is that there is room for YOUR feelings too. There are 5 key components. I won't go into detail cause you can read about it but the essence is you find and acknowledge the other person's truth, you imagine and state what they may be thinking and feeling, you ask them if you are getting it right? Then you say "I feel..." and share your feelings on the matter. And then end with something positive about them. In your case it might be something like:
"Hey man, I wanted to talk to you about the other weekend when my hangover got in the way of our plans. You're right to be upset with me. We had plans and I was a little too (tired, cranky, whatever it is) to really spend quality time with you. At first I was surprised that you were so upset but then I tried to imagine what you were feeling and I realized you might have thought I didn't put enough priority into our friendship and you might have been feeling hurt and even angry. Am understanding right, or is there something else?" Then let them talk and acknowledge whatever they tell you by paraphrasing it. Then you say how you feel "I feel a little _____ because_______". But you know I really love you and our friendship is important and I feel really grateful that you told me how my actions made you feel. Next time I'll plan better so that I can really be there for our time." Or something like that.
BUT BUT BUT...
If your friend is controlling or otherwise makes YOU feel unvalued....protect yourself and your rights too. Listen to if you are feeling angry or hurt and what that might be about. Maybe this friend tramples your boundaries and you need to speak up and make sure you matter.