City's thoroughly deserved 4-1 victory was built on a quick start and a dominant display in midfield, and Moyes admitted his side weren't strong enough to match the Blues.
"We didn't play well," the manager told Sky Sports. "They were better and started much stronger, much quicker than us. I thought Manchester City were very good. We weren't, I've got to say, but Manchester City started the game really well.
"They got a grip of the game very early on. We didn't. We never really got to grips with their midfield players in the early part of the game, and because of that they started to get domination. We had to be stronger. We weren't.
"But great credit to the lads that they kept going, and kept working away and got a goal back. We'll get better. It's a long season to go, so we'll put this behind us and move on."
The Reds are back in action on Wednesday evening for the Capital One Cup clash with Liverpool at Old Trafford, and Moyes is intent on a quick return to winning ways after a painful afternoon at Etihad Stadium.
"Whether it's a derby or somebody else, you don't want to lose," said the Scot, "but it does make it worse when you want to do so well for your supporters. I thought our supporters were great today, under the circumstances. Whatever manager loses a game, you get on and try to win the next game. You just play the next game and see how you go. We'll do everything we can to win the next one."
More: Rooney: We must improve | Vidic says defeat was 'horrible'