Sunday's 1-0 defeat, courtesy of a Bernardo Silva goal, left Antonio Conte's side five points behind fourth-placed Tottenham with nine games to play, heaping further pressure on a manager whose long-term future was already uncertain.
Sky Sports pundits Jamie Redknapp and Gary Neville had earlier labelled Chelsea's display in their 1-0 defeat vs City as "anti-football" and "embarrassing" respectively, and Conte has since hit out at both Redknapp and Neville referring to them as "stupid".
A defensive-minded Chelsea failed to muster a shot on target and had only 29 per cent possession as they went down to Bernardo Silva's 46th-minute strike.
"I think you have to accept every criticism but I am not so stupid to play against Manchester City open and to lose 3-0 or 4-0", the Chelsea boss said in his post-match news conference.
Eden Hazard admits Chelsea didn't play "a good match" against Manchester City, and that their tactical approach may have been the cause. "But we haven't played a good game and for me personally, it's hard to play a good game when you only touch the ball three times".
"I think they showed the difference between them and us in this moment - 25 points is a big gap and I think that we can have regret for the other games but not for this because I think the effort of the players was an important effort". I never [said] we have to win the two games to achieve something.
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They remain alive in this season's competition but must find a way past Barcelona at the Nou Camp next week to reach the quarter-finals. "We have to respect that and give our best, no matter who is on the pitch".
Of course we have five away games left having now won eleven of our fourteen.
"I know the Juventus team that he played in and I was England coach against his Italy team". We need to keep the focus on this and win the next game and go step by step. If I remember well, a few days ago, Arsenal played twice against them, they conceded three goals in 13 minutes. But we should have tried to do that all game.
After the disappointment of last weekend, the likes of Oliver Giroud and Eden Hazard have called Conte's tactics into question, while Marcos Alonso has suggested that the squad is perhaps to negative when playing.