The manager has to man-manage the players. This role is as important as coaching/team selection/tactics etc. If certain players decided that they weren't willing to play for Mancini then the club is simply left with a 'him' or 'them' decision. The same scenario could again be repeating itself with Pellegrini.
Amongst other problems, we have a few players showing a distinct loss of form, which is unfortunate but hopefully temporary, and a few players that regularly offer unacceptable levels of motivation, effort and passion. The latter problem is far from temporary and unless it's sorted once and for all it's likely we'll never see consistency from one season to the next. Although there's not a gulf of difference between the ages of the players in our squad there's certainly a huge difference in the maturity and mentality on show. We have those players that let emotions control their input and motivation, and then we have the real class acts that understand the importance of remaining focused and simply work harder to overcome any loss of confidence or form.
I honestly don't know what the solution is but I'm ruling out tactical formation, fitness or the introduction of a couple more players as any kind of 'holy grail' fix to the problem. Formation doesn't make you be 2nd to almost every 50/50 ball, It doesn't make the team slow down unnecessarily when attacking and it doesn't stop some of the taller players from winning aerial duels and corners against far smaller men. Until we get commitment and passion from the complete squad anything else (tactics/formation/squad rotation/fitness etc.) will be of secondary importance.
It may well be that we haven't yet found the right man to handle some of the attitudes/egos within our squad, however I do have a modicum of sympathy with Pellegrini when he said after the derby 'I don't understand why a team plays so well in the first 20 minutes'. I can't disagree with that comment, as we didn't go a man down, we had scored the opening goal and looked like we were going to steamroller them. I didn't notice any huge tactical change made by the rags to suddenly shift the balance of power. Baffling indeed...