City had 25 shots against Jose Mourinho’s side, but only managed to hit the target three times in 90 minutes.
The visitors created the more clear cut chances, having 18 efforts at Joe Hart in the City goal, as well as hitting the woodwork three times.
Pellegrini pointed towards the absence of crucial players, with both Sergio Aguero and Fernandinho missing the match through injury.
“We had clear chances to score at least two goals but didn’t do it, and they had two or three shots against the post,” the Chilean told Sky Sports.
“It was a very close game to play against Chelsea without (Sergio) Aguero and Fernandinho.
“It’s important to note that we were missing them, also Nasri and Javi Garcia. We had to change the midfield.
“It was an important game but we’ll continue and we’ll see. We’re just two points behind Arsenal.”