After being held to 2-2 draw at CSKA Moscow in the UEFA Champions League last week and losing 2-1 to West Ham in the Premier League, City crashed out of the League Cup at the hands of Alan Pardew's side on Wednesday.
The holders fell behind to a Rolando Aarons strike in the sixth minute at the Etihad Stadium, before Moussa Sissoko made sure of Newcastle's progression to the quarter-finals by adding a second goal 15 minutes from time.
City's defending was questionable for both goals and Pellegrini is worried about his side's current slump.
"We are conceding goals," he told BBC Radio Five Live. "We are not moving the ball as fast as we normally do.
"It was not a good week. We drew in Russia and have had two defeats but we must continue trying to recover, to think about the future."
Asked how he thought his players would react in this weekend's Manchester derby, Pellegrini added: "We will see on Sunday, we will try to react as soon as we can."
City have won their last three games against neighbours United.
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