Maurizio Sarri remains unsure whether Chelsea are serious contenders for the Premier League title despite his team moving up to second in the table.
Alvaro Morata struck a double and his fellow Spaniard Pedro was also on target in a 3-1 win at home to Crystal Palace on Sunday, the Blues' fourth consecutive victory in all competitions.
City, Liverpool and leaders Manchester City - who are two points clear at the top after thumping Southampton 6-1 - are all unbeaten after 11 rounds of fixtures.
But Sarri is not yet convinced Chelsea, who have won the title in two of the last four years, are ready to be considered challengers for City's crown.
"I don't know, I don't know," Sarri said at his post-match news conference.
"At the beginning, we knew very well that there was a gap. There was a gap last season, 30 points. So I think that, at the moment, we need only to think... to try to recover the large part of this gap.
"I hope to recover almost all the gap, but I don't know. I think it's very difficult to cover 30 points in six months, but we are trying."
Chelsea's latest win means Sarri has gone unbeaten in his opening 11 Premier League matches, the first manager to do so since Nottingham Forest's Frank Clark 24 years ago.
"I am really very proud, but I am very proud to be the coach of this team," Sarri said. "The record is not one of the coach, but of the team.
"I was lucky. I have very good players, and my players, in the last two months, were able to win also without a great level of organisation from the tactical point of view. I was lucky, I think."
Palace have lost four of their last five matches in the Premier League, slipping to 14th in the table, but Roy Hodgson does not feel the Eagles are in trouble.
"The teams who are in the second half of the table don't get that many points against those in the top half, especially at the moment given those teams are sweeping everyone in front of them," Hodgson told reporters.
"We put in a good performance last week against Arsenal, and again today. We can only hope to give those types of performance and hope luck goes our way.
"It doesn't really matter where you are at Christmas. We were rarely outside the relegation zone last season but ended up 11th. We've missed chances, yes, and been a bit unlucky, yes. We don't have as many points as we should have, yes.
"But let's see where we are after 38 games. It's important to keep going irrespective of what happens in the next few games."