Was the run earned or unearned?This is the key to your post. All the runs before really don't matter, because your DD gave up the "winning" run. I know it doesn't taste good but it's a fact. Even if you rallied back and scored 5 runs in the last inning, your DD gave up the tie breaking run making it 6-5.
Being a pitchers parent myself I am very sensitive to the blame game. You win as a team and you lose as a team. Does the pitcher sometimes lose the game all by themself? Sometimes. Does the pitcher sometimes win the game all by themself? Hardly ever. Maybe a 1-0 game that they produced the 1 run in but that's about it.
I guess I'm not very good at the crutch. If I think my DD lost the game I try to learn from it and hope that she learns from it without me having to point anything out. If I think she didn't lose the game all by herself then I hope that she learns from what she did wrong and understands that she can't do everything herself. It's a bizarre game but confidence, mental strength, and belief are all part of it. The daughter may have given up that 6th run but maybe she pitched the situation perfectly and the shortstop launched the ball into right field. The pitcher can't blame herself for that. Instead she has to believe that if she keeps doing things right things will turn out. Otherwise she starts to believe that she has to do it all and that's a recipe for disaster.