I have a similar problem, but reversed, in a way. I can't handle playing in a 1v1 situation, where it is just me against some stranger, because if I lose there is no doubt in my mind that it is because I failed and my opponent outplayed me. That is part of the reason why I quit Starcraft 2, I just couldn't take it anymore, and 2v2, 3v3, 4v4 are not as good.
However when playing team games, such as Dota 2, I used to play MW2/3 etc., I have no such anxiety. Even if the team loses, it's rare for ALL the blame to be on one person, and even if I end up in such a situation(which I do not think I have), it's better than carrying all the blame every single time you lose.