The Brazil international missed his side's 1-0 loss to Chelsea at the Etihad Stadium on Monday night, which ended City's 100 per cent home record in the Premier League.
Pellegrini revealed the full extent of Fernandinho's injury and also defended his decision to field Martin Demichelis in midfield in the former Shakhtar man's absence.
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“Fernandinho has a muscle injury, we’ll see tomorrow how long he’ll be out for. I think it’ll be a matter of three or four weeks.
“This game was not a problem of the midfielders. I didn’t make the other two substitutions because I didn’t think we could change the game by doing that.
“For Chelsea it was an essential game. It was important because we could have been six points ahead but we’re just two points behind Arsenal in second.”
Pellegrini is currently having to contend with a host of injuries to first-team players, and admits the growing list of casualties – which now includes Fernandinho – contributed to their defeat.
“Well I think that of course Fernandinho is an important player for us,” the 60-year old continued.
“Not only him, you have to add [Sergio] Aguero, [Samir] Nasri and Javi Garcia – Milner was not 100% so he couldn’t start, Alvaro Negredo wasn’t 100% either.
“That’s too much of an advantage for an important team like Chelsea.
“We lost today against a good team who played well and I thought we deserved at least a draw but they had the luck to win it.
“They scored a beautiful goal, not an easy goal, he hit it from a long way out with the outside of his foot but before their goal we had clear chances to score, so I don’t there was a problem with the way we played.”