The Chilean refused to acknowledge his counterpart at the final whistle and also felt his side was in "complete control" of the game despite slumping to defeat
"I didn't shake hands," he said. "I didn't want to".
The Chilean refused to acknowledge the Chelsea boss after the game, heading straight down the tunnel in west London after seeing Fernando Torres pounce on a defensive mix-up late on to secure victory for the Blues.
City had looked to be grabbing a point after Sergio Aguero canceled out Andre Schurrle's opener but Torres' 90th-minute goal was enough for victory and moves Chelsea up to second in the table, just two points behind leaders Arsenal.
Pellegrini's men, meanwhile, drop to seventh after suffering their third Premier League defeat of the season already and the manager felt his side was unlucky to lose.
"We had complete control of the game. We repeat the story of our other two [league] defeats," he told reporters.
However, the City boss revealed little when asked about his reaction to Torres' winner, which occurred after a mix-up between Matija Nastasic and goalkeeper Joe Hart.
"I will keep it private. From tomorrow we will begin to arrange how to avoid the mistakes we have made," he added.
"We are losing stupid points. We have time to arrange and we will try to arrange. I am happy with how the team is playing."