Mourinho jumped into the crowd to celebrate Fernando Torres' stoppage-time winning goal as the Blues moved up to second in the Premier League table with a 2-1 victory over the Citizens at Stamford Bridge.
Pellegrini insists that he was not surprised by Mourinho's celebrations, but did not feel in the mood to acknowledge the Chelsea boss.
When asked why the two managers didn't shake hands, Pellegrini responded: "I did not want to. I did not expect anything different from him. It is normal."
Mourinho replaced Pellegrini as the head coach at Real Madrid in 2010, after the Chilean was sacked despite gathering a then-record points total with the La Liga giants.