This is the hope we all had for Hodgson, though, is it not? That he was only coaching and playing that way to reflect the quality of players he had worked with. But no, he stuck with his own methods, and brought the level of the players down. Moyes is the same. Coaches have their methods because they believe in them and believe those methods are transferable. Rafa doesn't change from one team to another. Mourinho doesn't. Guardiola will do the same things at Bayern as he did at Barca. Moyes will do what he did at Everton. And it won't be enough.
It's less to do with the technical level and more to do with the habits of the players. Everything they did on the field for Ferguson was drilled into them day by day, session by session, exercise by exercise, until all of those visual and tactical triggers became second nature. Now that flow of information will not only be disrupted, but changed almost completely. They will effectively be starting at the start again, and have to learn a new way of playing, a new set of triggers to look for, a new way of training, and a new way of defending. These transitions are made smoother when you keep the previous coaching staff and work little by little. This is what happened, to a degree, with Rodgers, when he came in. New staff, new methods, new style of play and new set of triggers. The only reason he had some leeway is because we haven't challenged for the league since Rafa, and had been out of the top four. Moyes is taking over the reigning champions, and so his margin of error with the players is virtually non-existent. If he gets it wrong and takes a step in the wrong direction, he'll rapidly lose the belief of the players, and they will put on sub-standard performances in games, consciously or unconsciously.