The Italian was appointed in July after compatriot Antonio Conte was sacked following the Blues' fifth-placed finish last season, 30 points behind champions City.
Chelsea enjoyed an 18-match unbeaten start to the competitive season, after losing the Community Shield to City in Sarri's first game in charge.
Two defeats in the last three league games, to Tottenham and Wolves, mean Chelsea sit fourth, 10 points adrift of leaders City after 15 games.
"I was sure that sooner or later we'd face problems, but I thought it would be in the first two months," Sarri said.
"The first two months we played well, we gained points. And so I thought that the problems would arrive in November and December. I was sure.
"When you change the way of playing, the way of football, you need to change the mentality.
"You need to change the mentality in 25 minds, so it's not a short way. It's very difficult."
Pep Guardiola's City have won 13 of their Premier League games and are unbeaten in the top flight since April.
Sarri, who has experienced defeat to Guardiola with Napoli and Chelsea, was asked how his side can beat City.
He added: "Against Guardiola I lost every match, so I don't know. You have to ask somebody else."
City are the best team in Europe, Sarri says – and that is his target for the Blues.
He added: "It's a very difficult match against, maybe, the best team in Europe at the moment.
"It's impossible to beat them in a long period, of course, in this moment. But in a match, everything can happen.
"In 90 minutes anything can happen. We know it's very difficult but we have to believe in it."
Sarri accused his Chelsea players of a collective "blackout" at the first sign of trouble against Fulham, despite a 2-0 win, and against Wolves.
The Italian said: "We have a problem to manage the match at the moment. In the last two matches we played well for 55, 60 minutes, then the first difficulty we went in blackout.
"In the first match (against Fulham) we were lucky because they didn't score. In the last match (at Wolves) we were a little bit unlucky. For the opponents, five shots, only two on target. We conceded two goals."
Sarri struggled to explain the reason for the lapses.
He added: "It's not really very easy to answer. We didn't react as a team (but) as 11 players. In 11 different ways. So it's a big problem. We were not able to have the right determination to win the match."
Playmaker Jorginho is expected to return after being rested against Wolves.
Sarri's selection of Jorginho at the base of his central midfield, with N'Golo Kante further forwards, has been scrutinised.
The Blues boss has explained his reasoning and says the choice is only being questioned due to the defeats.
Sarri added: "The problem is only the results. When we won, the position of N'Golo was 'good'. So it's only down to the results.
"At the moment, we're not winning so it's normal that some players are playing very badly, some players are in the wrong position.
"I explained why, usually, Kante plays in that position. I have my opinion. I can understand that you or someone else doesn't agree. But I explained very well why."