Manual Response For Apology

When I apologize, if it wasn’t something that bad, I assume the other person will reply with accepting some responsibility in response and when they don’t I am annoyed. This is partly cultural I guess. I know I am in the wrong with my reaction. I guess I need to just focus on my part but that feels like I am being taken advantage of when the other person accepts no responsibility. I wonder if my apology is insincere. I don’t think it is. I guess I just thought it was obviously more their fault than mine so when I apologized I didn’t expect them to be cold. I feel like I am right and wrong at the same time. Advice?