The reigning champions were on top from the outset, but Pep Guardiola's decision to play Raheem Sterling through the middle in the absence of the injured Sergio Aguero failed to pay dividends and they were unable to regain top spot from Liverpool, who beat Bournemouth 4-0 earlier on Saturday to edge a point clear.
"I said that is not going to happen". "I said many times, I'd like to have Kevin available, but we try to not put pressure on one player and instead on everyone involved to make a good team". "We are not here to be Invincible; we are here to be champions".
Sarri's positive start to life at Chelsea has hit something of a snag in recent weeks, with two league defeats from their last three games.
City remain the odds-on 1/3 favourites to become the first club to win back-to-back English titles in 10 years, however there's been a significant move behind them in the betting, as Liverpool have been cut from 4/1 to 5/2 to lift the Premier League trophy for the first time.
They had dominated proceedings until just before the break when Eden Hazard set up the normally goal-shy Kante to fire home brilliantly into the roof of the net.
"To come here and play how we did, despite the scoreline, is never easy", he said.
"We won today but we have to say that we were a bit lucky in the first 25 minutes because they could have scored".
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"I'm happy for the win because it's hard to win against Guardiola's team", he added.
"The way we played in the first half was incredible", Guardiola said.
Kante and his teammates came through a gruelling test to take all three points against Pep Guardiola's City team and the French World Cup victor spoke about this after the game. "Now we have to find this kind of motivation and need to play with this level of determination and aggression in other matches".
Sarri's praise of Kante's positioning alongside Jorginho in Chelsea's midfield was in stark contrast to the criticism he dished out to the Frenchman after Chelsea's defeat to Spurs.
Hazard was finally fed the ball to feet inside the City box and his pass picked out Kante, who side-footed the ball high past Ederson.
Kante, with two goals, has already surpassed his best goals total for a Premier League season. "Sometimes, I have chances in this position to score".
Ralph Hasenhuttl got off to a awful start as Southampton manager as Callum Paterson scored the only goal in a 1-0 win to move Cardiff three points clear of the bottom three and leave Saints level on nine points with Fulham.