Mancini is a weird manager to talk about, he is both great and also terrible at the same time based on which team he is managing. For example he was so great for City, but then he couldn't find any other job and went to Galatasaray in Turkish Super league, and got fired there. Imagine a manager who has insanely good success at City and then fail to find a team to hire him and go to a mediocre team and fail there... that rarely ever happens, not that back to back at least. Then he went to Inter and was decent enough, not great but not terrible, now he is amazing with Italy and they are playing the best national team ever with him at the helm.
So, I really do not know how he would be in United. He could be their best coach since SAF, or he could be worse than even OLE and both look like a possible outcome right now. He is an enigma that nobody could figure out.
But was it solely the coach's fault?
Coaching a team like City that has high performance players is "easy", of course it requires a lot of responsibility.
However, training a team of "bad players" and hoping to obtain good results is much more difficult, especially if the team doesn't have the resources to invest in new players or even in the physical preparation of them, as we know that a good structure makes a lot of difference.