Moyes never got a real chance at Man Utd.
He inherited a squad that was at least a year "off their sell-by date", that Ferguson had kept "alive" for one last season by sheer will power (and charisma).
Then Moyes came in, got no help on the transfer market that Summer. The team desperately needed a handful of players that year, IMHO, and he got Fellaini at a very premium price. Now Fellini was a good player, but he was not a man who single handedly could go in and lift a whole team.
The only (big) mistake I think Moyes did was insisting on bringing in a lot of staff with him, dismissing some of the staff that knew Man Utd (both the remaining team and organisation as a whole), and thus not really take advantage of some of the continuity he could have drawn from...