Nasri has been ruled out for up to eight weeks after suffering a partial ligament tear in his left knee following a shocking challenge from Mapou Yanga-Mbiwa in City's 2-0 win over Newcastle on Sunday.
The Frenchman has played a key part in City's good form, which has seen them go 10 matches unbeaten in the English Premier League to be within a point of leaders Arsenal.
Pellegrini, whose side face Blackburn in a FA Cup replay on Wednesday, said Nasri would be missed.
"He is a very important player for us. He was also playing in a very good moment so we hope he can come back as soon as possible," the Chilean said.
"But I think that less than six or seven weeks would be difficult."
Pellegrini's team were held to a 1-1 draw by Championship outfit Blackburn to force the replay at Etihad Stadium.
He warned his team they would need to be at their best if they were to advance to the fourth round.
"(Blackburn) didn't surprise me. I think that they played a very good match at home," Pellegrini said.
"I am absolutely sure that tomorrow we must do a very good game if we want to win because they are very motivated, a strong team and they play exactly the way they want to play.
"We must be very attentive tomorrow in defending and in counter-attacks and defend the set-pieces. We need to try and score a goal and it will be very close."
Pellegrini talked up the importance of the FA Cup, saying he wanted to win every trophy available to his team.
"It is very important. It is very important not only because it is an important game but we have a lot of games also," he said.
"We are for the moment the only team still in the four competitions and we will try and we want to win things."
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