A 3-1 win over West Brom on Monday saw City close to within six points of Brendan Rodgers' men, and they still hold a game in hand.
Pellegrini felt postponed games had made it difficult for his side, but wants them to challenge Liverpool and capitalise should the table-toppers slip up.
"We know that at the moment we had two or three games postponed and it was very difficult for us to be at the top of the table and to feel that we're the team that has more of a chance," he told a news conference after his side's win over West Brom.
"At the moment we lost the game against Liverpool, we know we don't depend on what we are going to do from now to the end of the season, but we have a duty and that is to win our games."
Pablo Zabaleta and Sergio Aguero struck in the opening 10 minutes against West Brom at Etihad Stadium.
Graham Dorrans pulled a goal back for the visitors soon after, only for Martin Demichelis to restore City's two-goal lead nine minutes before the break.
Pellegrini said City's first-half performance was consistent with their home efforts this season, having won 15 of 17 league games at Etihad Stadium.
"I think that the first half we played very well, we scored three goals and we had clear chances to score," the Chilean said.
"I think the first half was the team we saw over the whole season here at Etihad.
"Maybe the goal they scored made us a little bit more nervous. In the second half we didn't play so well with the ball but we kept the score. That is very important also."
Pellegrini also refused to comment on reports under-fire Manchester United manager David Moyes is set to be sacked.
