Moyes greatest strength at Everton and the biggest reason for his success was always his transfers. He constantly plucked top class players from nowhere, paying tiny amounts. Despite Fellaini's failure it should be one area to have faith in the manager.
In fact, if anything I feel like the current mood around United and in the summer have been really holding Moyes back. The constant demands for world class, £30, £40million signings is neutering Moyes main advantage. He doesn't have to root around in League 1 for 500'000 signings to pick out bargains, these days a £10million player is cheap. Newcastle themselves have made great progress picking up players in that bracket, Cabaye included. Not to mention that neither Dortmund nor Juventus splashed out the cash until very recently, they relied on similar purchases and youth.
Yes, eventually to move up you have to bring in the big money purchases, as Juve found with their striker situation, but United aren't at that point, not to mention they just bought two world class players last season in Kagawa and Van persie. Let Moyes build his squad first, then go for the Fabregas's, the Falcaos and the rest. Any manager can be successful throwing around that kind of cash, even Mancini won the league.