The Red Devils manager suffered the sixth Premier League home defeat of his first season in charge as Manuel Pellegrini's near neighbours eased to a 3-0 victory at Old Trafford on Tuesday night.
For the second time in 10 days, Moyes found himself explaining the reasons behind a heavy home defeat to a regional rival - Liverpool having won by the same scoreline against the reigning champions.
Two goals from Edin Dzeko and a late Yaya Toure strike did the damage, but in truth City - now 5/6 title favourites with Sky Bet - were superior in every department.
Moyes told Sky Sports: "I think we've played a very good side and it's the sort of standard and level we need to try and aspire to get ourselves to at this moment in time.
"I think we need to play better. We're needing to come up a couple of levels at the moment and we're not quite there.
"We didn't start the game well, in the first 15 minutes they were very good and we've conceded a goal in 45 seconds so we've not given ourselves a fighting chance.
"I thought we grew into the first half and got better and until the second goal we had a chance, but on the night we didn't do well enough."
In the post-match press conference, Moyes attempted to defend another poor performance from his side which left them 12 points adrift of fourth, with Chelsea a distant 18 ahead.
"I take responsibility for the team, I always will do," said the Scot, whose side have taken just seven points from 13 games against the present top nine.
"Everyone knows this is going to be a job which is going to take a little bit of time to get the way we would like it, but that is the job and I recognise that.
"I thought it would be a tough year for us, no doubt about that, but I hoped it would be much more competitive and closer to the top of the league than we are at the present time."
Moyes has consistently shouldered the blame and deflected criticism away from his players and he did so again, although even he admitted he did not understand why they were not up for the game against their rivals from the off.
"We never started well. We never gave ourselves a great opportunity to get into the game," added the Scot.
"Manchester City started really fast and conceding a goal after 30-40 seconds made it difficult.
"I just think we never came out of the blocks. 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."