Well, likewise, players who have a manager whom they feel doesn't have their back are not going to perform as well. I have said this about the influence that I think Bobby Valentine had on the team. It works both positively and negatively.
However, it is an ongoing thing that shapes itself over the course of a season. It's not something that can be readily turned on or turned off, or kicked up a notch or toned down a notch on a whim. In other words, a manager cannot get a player to raise his game to otherworldly for the postseason, just like a player cannot raise his own game to otherworldly for the playoffs. The idea that a manager 'did not have his team ready for the playoffs' is just way off base.
I agree that some handle pressure better than others. As I've said before, players who can't handle the pressure, ie the chokers, either don't make it to the bigs or don't stay there very long.