Sarri is under immense pressure after his side were beaten 6-0 by the reigning Premier League champions.
It is the first time Chelsea have conceded four goals in back-to-back away games in the Premier League after a 4-0 defeat to Bournemouth recently.
Sergio Aguero bagged a hat-trick as Guardiola’s team dominated against the Blues.
And Sarri did not hang around to congratulate the Spaniard, walking straight down the tunnel at the final whistle.
That left Chelsea assistant Gianfranco Zola to shake Guardiola’s hand with the City boss looking bemused.
Chelsea were never in the game at the Etihad, going 4-0 down inside the first 24 minutes.
Raheem Sterling also got two with Ilkay Gundogan bagging the other.
The win puts Manchester City back to the top of the Premier League, level on points with Liverpool who have a game on hand.
But focus remains on Sarri, with the Italian in his first season at Chelsea.
He replaced Antonio Conte at Stamford Bridge in the summer, though has been regularly criticised for his lack of control.
And after seeing Sarri snub Guardiola, football fans gave their say on the Italian.
One wrote: “Absolutely embarrassing from Chelsea. Sarri didn’t even give pep a handshake.”
Another blasted: “Sarri no handshake. Shameful.”
And a third commented: “Sarri just walked off without a handshake. Sore.”
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