Enduring a difficult start to life at Old Trafford, and with Sir Alex Ferguson casting a huge shadow, the last thing Moyes needs is mutiny. And especially from such a senior player, one of the most influential personalities in the dressing room.
Evra has cause to be upset.
He will know how desperately Moyes pursued Leighton Baines this summer. And the last-minute bid for Fabio Coentrao looked like desperation.
It appeared as if Moyes was willing to move heaven and earth to sign another left-back and that's not a huge vote of confidence for the one already there.
At 32, Evra will need to be replaced sooner rather than later. But he's been a fantastic servant and deserved more respect.
He's barely missed a game since establishing himself as first-choice. His Premier League appearance record over the last four seasons reads 38, 35, 37, 34. For a 38-game competition, and in a position as energy-sapping as full-back, that's phenomenal.
Evra is a very proud man, never shy in answering back to his critics.
The Baines saga will have hurt because as much as Moyes tried to insist he simply wanted to add competition, the Frenchman will know that the Everton left-back wasn't going to come to Old Trafford to sit on the bench.
But Evra's desire to stay at United will allow Moyes to take a different approach.
He will need to sign a left-back at some stage, that much is clear. Alex Buttner and Fabio haven't shown enough to suggest they could take over on a permanent basis and youth team product Zeki Fryers has long departed to Tottenham.
But instead of opening the chequebook to sign 28-year-old Baines, he could now switch his attentions to 18-year-old Southampton full-back Luke Shaw.
Shaw, still learning the game, might be convinced to share the role with Evra for a season or two in a way that Baines probably could not.
Evra, meanwhile, would benefit from having a rest every now and again. In the past, a lack of competition has meant he's had to play every game, regardless of form or fitness.
United will face competition from Chelsea for Shaw, should he decide to leave Southampton.
But he should be high up on Moyes' shopping list as well. At least a few places ahead of Baines.