Neville didn't start it. He is a moaner, he does it nearly every game I watched since he came to the PL.
I agree that it's a form of caring, but it also drags the team's morale down and it's contagious, especially when he's not been particularly good for quite a while. Whatever mistake happens on the pitch, you sort it out after the game between closed doors. In the meanwhile you motivate your partners and try to make up for their mistakes, you don't berate them in front of thousands of spectators. His constant arguing with the referee also gets on the nerves. Him and Ronaldo are the best players and their behavior has a massive impact on the other players, like it or not.
Having them lashing out is never a good thing, and I'm fairly certain that the atmosphere in the dressing room isn't rosy at all.