Been in both spots, as a player & a parent & I always come back to this thought. As a player, you are never really perceived as good or as bad as you view your own performance. Same as a parent interpreting their kids performance on the field.
Think about it. If you are watching a game & a kid you know is a good pitcher is getting shelled, you may think; "Oh well, tough day for Johnny, but he will be back next time. No big deal." On the other hand, if you are the player or parent you are living & dying with every pitch. You imagine an intense focus on your performance & the whole world is witnessing your implosion when things go bad. The truth is that most others pay scant attention & the episode, although excruciatingly painful, is quickly passed & we are on to the next inning, game, at bat etc.
The players who excel are somehow able to shed these negative feelings, learn from the experience, retain their confidence & thrive in an incredibly difficult game. I do not think the parents ever truly learn to cope