The Blues dropped down to fourth after their 2-0 loss to the reigning Premier League champions, and face a battle for Champions League qualification with both Tottenham and Arsenal finding form.
And the Spaniard has described the west London outfit's showing at the Etihad Stadium as not good enough.
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"On Sunday it wasn't enough, the job that we did, and what we have to do now is just carry on, the season is not finished yet.
"When you play teams like Man City you have to perform at your best. We tried but in the first 25 minutes they were better at pressing us.
"At the end of the first half we changed the game a little bit and after we had a few chances, and in the second half it was an important moment with the penalty and Joe Hart did a very good save."
Mata's team-mate Gary Cahill, meanwhile, expressed his belief that fixture congestion handed Roberto Mancini's men the advantage.
"At the start of the season we had spark and we had zip and sometimes a little bit of fatigue plays its part," said the defender," he said.
"Man City had a clear week before the game and we didn't and they were a lot fresher and sharper than us.
"It does take its toll, we have not had a clear week for many weeks and you are expected to go into games 100 per cent fresh, trying to push on for every competition.
"You don't want to make excuses but it is a fact. It is something we have to deal with."