Nastastic suffered the injury during the second half of City's 1-0 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.
- Sports & Recreation