City struggled to a 1-0 win thanks to Yaya Toure, but not before Dzeko missed from two yards out.
Pellegrini said he had not lost any faith in Dzeko - who has still scored 17 goals this season - after his remarkable miss.
He said: "Every player can have a bad day. Maybe he had a bad day, maybe he was nervous after he failed that goal but I will continue trusting in him."
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