Antonio Conte's side took a giant stride towards the Premier League title with two goals from Eden Hazard.
Sergio Aguero struck for City but it was not enough to close the gap on the Blues at the summit.
Chelsea have denied that they were to blame for the altercation at the final whistle.
Chelsea player ratings against Man City
Wed, April 5, 2017
Click through the gallery for the Chelsea player ratings against Man City
1 of 11
Thibaut Courtois – 5
But The Sun claim a Chelsea coach told a City individual "we f*** you up the a***" in the tunnel.
It is said he made the comments in Italian, much to City's displease.
Guardiola witnessed the war of words and was furious at how Chelsea rubbed salt into their wounds.
Get Quotes on Home Insurance
Antonio Conte and Pep Guardiola clashed as Chelsea beat Manchester City
Eden Hazard scored twice as Chelsea battled past Manchester City
However, he continued into the dressing room without getting involved.
The City boss was seen actively remonstrating with Conte during the clash.
But the Chelsea boss sidestepped the whole issue having already marched into the dressing room after the game.