United were soundly beaten 3-0 by their title-chasing neighbours at Old Trafford on Tuesday night as Moyes was given a stark reminder of where his side should be.
“I think we’ve played a very good side, playing at the sort of level we’re aspiring to,” said Moyes. “We need to come up a couple of levels ourselves because at the moment we are not there.
“I take responsibility for the team and always will do. I have to be the one who picks the players.
“I still think there are a lot of good players in this squad, but some of them could play better.
“I thought it would be a tough year for us, but I hoped it would be much more competitive and we’d be closer to the top of the league than we are."
Given this season's form, United were always going to be up against it when faced by an ebullient City side, but their task was made even more difficult once Edin Dzeko put City ahead inside the first minute.
Dzeko grabbed a second early in the second half before Yaya Toure sealed victory for City late on. The win saw Manuel Pellegrini's side move back into second, three points behind leaders Chelsea, but with two games in hand.
In terms of their local rivalry, the gulf between the two teams is evident: City find themselves 15 points ahead of United with nine games to play.
"I just think we never came out of the blocks," Moyes said. "You prepare the players, you warm them up, you do all the things to have them ready, but we just never started.
"It gave them (City) a real big lift to get a goal so early on.
"We had to try to make sure we got through that 10-15 minute period when they were out of the blocks.
"After that we weathered it and got ourselves back into the game and finished the half quite strong.
"The key to it was not to concede a second goal so we could always give ourselves a chance back in there, but I didn't think we started the second half well.
"We brought pressure on us by our play and in the end we conceded a corner just before that and there was another one and then that led to a goal.
"It was obviously poor marking and we should have done much better."
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