City had 25 shots in Monday night's Etihad Stadium showdown against their title rivals, but only managed to get three on target in the 90 minutes.
The visitors were more dangerous, with a third of their 18 shots testing Joe Hart in the City goal and a further three hitting the woodwork.
Even then, City had chances to snatch an equaliser at the death as David Silva and Stevan Jovetic both came close to finding a way past Petr Cech.
Pellegrini pointed towards the absence of two of his key players - Sergio Aguero and Fernandinho - both of whom were sidelined 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."