It depends on each individual actually. When something bad happened on me, I tried to think that it's not someone's fault. Shit happens. That's all. If I keep trying look for whose fault it is, then the problem would never be solved. And blaming myself isn't helpful too after all. When I'm having problem, the first thing I need to do is find the solution. And evaluate myself. Think why it happens. If it's clear that I did a mistake, then I should apologize. If it's clearly someone's mistake, and he/she didn't apologize for it, don't blame him/her straight away but try to speak to him/her for the helpful solution. It takes a lot of patience for not blaming someone.
When will people be tired of blaming each other?
Stop blaming is a part of being mature.