Is It Worth it?

Hi. Does anyone have any advice for dealing with someone that will not accept that they were in the wrong by letting me get in trouble for their mistake? I go told off for supposedly leaving a window open after a shower, I was sure I had but doubted myself briefly because I sometimes do things on autopilot and did not want to blame anyone. I found out it was someone else, which annoyed me because I felt like I had been told off for something I did not do. So I was trying to tell the person who had done the wrong thing that I was annoyed because it felt like I had been told off for something I did not do, and they had a go at me for trying to give them stress over it. They had no empathy for my upset and thought I was being antagonizing, when I just wanted to have an adult conversation which is what everyone wants me to do so I do act like a child in the hope that they would listen. And what doesn't help is that I couldn't tell the other person it was not me because there have been incidents before when I cannot remember or haven't done the wrong thing and no one believes me. I feel like I am blamed for something I did not do, I want to get myself in the clear but know that they will think I am an idiot or only caring about mjy feelings when I feel like they don't care about mine in that moment.  So, any advice on how to deal with people who want me to shut up and are unwilling to listen to me over incidents like this?