The United boss watched his team go down 4-1 at the Etihad Stadium, with Wayne Rooney's superb late free-kick nothing more than a consolation goal.
Speaking to Sky Sports afterwards, Moyes admitted: "We didn't play well; they were better. They started much stronger and much quicker than us.
"But we'll get better - it's a long season to go. We'll put this behind us and move on.
"I thought Manchester City were very good. We weren't, but City started the game really well. We really could have done with coming in at half-time 1-0, losing the second goal just before half-time changes it a little bit. Nevertheless, they came out strong again in the second half.
"I think they got a grip of the game very early on, and we didn't. We never really got to grips with their midfield players in the early part of the game.
"Because of that, they started to get domination. We had to be stronger, but we weren't. But geat credit to the lads that they kept going, kept working away and got a goal back.
"Whatever manager loses the game, you try and win the next one - nothing changes."
When asked about Rooney's individual performance, Moyes added: "I would say Wayne Rooney's performance today was outstanding. He certainly didn't deserve to be on the losing team. He was first class."
United have seven points from their opening five games, having lost to rivals City and Liverpool, and Moyes repeated his unease at the testing start allocated to his side by the fixture computer.
"We did say it was a difficult start, didn't we? I said at the time, the way the balls came out of the Premier League bag, I was't convinced... and I'm still not."