They moved back to the top of the Premier League table on goal difference, albeit Liverpool having a game in hand.
"All I can do is apologise to the fans because it is not acceptable", he said.
A mischievous member of staff at the Etihad mocked Chelsea by playing One Step Beyond at the final whistle.
"They beat us at Stamford Bridge and against Napoli [Sarri's old club] last season they were tight games - in moments of those games, they were better than us".
Raheem Sterling started and ended the scoring and Ilkay Gundogan also netted in the first quarter of the game as City ended what could have been a testing week with a trip to Everton in between the visits of Arsenal and Chelsea with maximum points.
Cristiano Ronaldo vs Anthony Martial - who did it better against Fulham?
But these big games coming up will determine where we end up. "We gave them the first 10 minutes, maybe played into their hands". Martial had already set up the opener for Pogba in the 14th minute when he produced his moment of magic nine minutes later.
Aguero should have had even more than three as the Argentine missed a glorious early chance and hit the bar in the second-half in a humiliating afternoon for Maurizio Sarri's men. Kevin De Bruyne released Bernardo Silva down the right with a cleverly-taken free-kick and the Portuguese cut back for Sterling to smash home.
In the past week City have beaten Arsenal at home and Everton away before taking Maurizio Sarri's side to pieces with four goals in the opening 25 minutes.
Both Aguero and Shearer have 11 Premier League hat-tricks to their name. Chelsea midfielder Ross Barkley inexplicably headed a clearance back toward danger and Aguero pounced by shooting on the turn.
City eased off for the remainder of the first half, and Chelsea striker Gonzalo Higuain even managed to test goalkeeper Ederson with a sharp volley. Sterling was brought down in the box by Cesar Azpilicueta and Aguero stepped up and sent Kepa Arrizabalaga the wrong way from the spot.
"The first five or six minutes went well but that is not enough". But on the hour, Leicester was awarded a penalty when defender Jan Vertonghen knocked over James Maddison. "We wanted to press them at the beginning of the action but the plan was completely ruined because we concede after three minutes".