NLAS,
I think this is where trial, error and self forgiveness have a big place. Also note that someone else's not liking the fact that we just stood up for ourselves does not equal being wrong! Sometimes they did certain things that were wrong because we let them and they don't like seeing the "rules of the game" changed to reflect the truth. Will a person content to violate some aspect of a relationship just "flip a switch" when you bust them and apologize? Not likely!!
When it comes to the real screw-ups...
We were not allowed to screw up in our family and screwing up could happen even when we took all the right measures to please a normal person. As an adult, I had to learn to say sorry and let that be enough when something didn't go well. Needless to say we are hyper-sensitive to the guilt from screw-ups. While the person we offended may be angry for a moment, our punishment of self can last for weeks.
For a normal person, "I'm sorry", or if we don't agree, "I'm sorry you feel that way", is all the acknowledgment we owe their feelings. After that we can take note of their preference and whether it is asking so much of us that we no longer wish to be around them.