The Premier League champions slumped to their second defeat of the season at the Etihad Stadium and Moyes revealed he had informed his team of just how disappointed he was by their performance.
"I’ve made them aware of that," he told reporters. "But if there is ever was a group of players I’d expect that from it would be a group of Manchester United players.
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"We’ll make sure we react. Every manager has bad results. I’m no different."
The Red Devils face Liverpool next in the Capital One Cup on Wednesday, having already lost to Brendan Rodgers' men in the league this season, and Moyes wants a better performance from his side at Old Trafford.
"I’ve been here before with Everton and never suffered a defeat like this," he added.
"So I just told the players, in the same way I would have told players at any other club, if I don’t think they’re doing it.
"They’re good players, they’re good pros, they know when they’re bang at it and when they’re not.
"City were the better team, they were stronger, they got control of the game and we found it difficult to contain them.
"I’m disappointed we didn’t perform. There was no reason for us not to perform, but it was one game. There’s plenty of time to come.
"We were second to things, in the first-half especially. We seemed to be a yard behind it and never got to the pace of the game right from the off.
"We had a good result in midweek and we wanted to build on that, but we never got to grips with it."