Nastastic suffered the injury during the second half of City's Barclays Asia Cup triumph over Sunderland.
The Serbian looked in pain and Pellegrini now faces an anxious wait to see what the damage is.
"The doctor has to see him tomorrow when we arrive back in Manchester," he said.
"I am concerned but it's better to wait.
"It wasn't the pitch though. He got a kick on his ankle but it was just part of the game."
At least in Joleon Lescott City have an obvious replacement should Nastasic be ruled out for any significant length of time.
They also have a trophy now thanks to Edin Dzeko's early goal.
Of equal importance to Pellegrini though were the performances of new boys Jesus Navas and Alvaro Negredo, who are slowly getting used to their surroundings.
"I know Negredo very well," said Pellegrini.
"When we brought him here we knew he was a successful player and in these two games he's demonstrated what he can do.
"Jesus is the same as Negredo. He gives our team a different option.
"He is very a difficult player (to play against)."
Sunderland manager Paolo Di Canio declared himself satisfied, despite the outcome, and said the pitch had not been quite as bad as he initially feared.
"The pitch was difficult but it was also difficult for them because they have fantastic ability," the Italian said.
"Thinking about it last night I thought it would be a worse pitch.
"But they put a lot of sand in the middle of the pitch and actually it wasn't that bad."
After rescuing the Black Cats from relegation last season, Di Canio has now had chance to make his mark properly.
"Some players still don't know what I want from them exactly but we still have a long time," he said.
"Even some top players are never going to change their mentality, but this process can be up and down.
"There is no way we are overtraining the players though.
"Last year some of them under trained.
"We have to be careful because we have a plan we know we can pay a price."