City boss Roberto Mancini accepts the Blues are now the underdogs to progress through to the Champions League knock-out stages - but he thinks it is still possible.
The 2-1 defeat to Napoli means City need a massive favour from Villarreal in the final Group A match while the Blues must also beat Bayern Munich at the Etihad Stadium.
"We should still believe because it is my opinion that Villarreal can get a result against Napoli," said Mancini.
"I don't think Villarreal will end up with no points at all and I certainly believe they are capable of a draw - maybe more - so we still have a chance, even though were are relying on another team.
"I don't think we deserved to lose this game, but at the same time, it is impossible for us to go and score three or four goals every game.
"We conceded two stupid goals because we knew Cavani likes the near post and for the second he had far too much room, so we didn't help ourselves in that respect.
We came to win because this is our mentality and it would have meant we went through tonight, but the Champions League is hard and we have a very tough group - but never say never
"We have one more game and everything is possible in football - as long as we believe in ourselves and that anything can happen. I think Villarreal will get a result against Napoli and then the rest is up to us."
Nigel de Jong was equally hopeful that the Blues can still progress, adding: "Napoli played well and took their chances well whereas we didn't take all of ours and that was the difference, I think.
"We had a lot of the play, but we didn't use the possession as well as we needed to.
"Now we need to unite as a team and get our focus back because we have one more group game left and while our fate is no longer in our own hands, there is still hope as long as we beat Bayern Munich."