Edin Dzeko slid in to give Pellegrini’s side an early lead at The Etihad, before Cheick Tiote had a goal controversially disallowed when Yoan Gouffran was judged to have interfered with play from an offside position.
Alvaro Negredo’s goal after a swift counter-attack then sealed victory for the visitors in stoppage time.
“It was a very difficult game and it’s a very big result as we know it’s a tough place to come and win,” Pellegrini told BBC Sport.
“Nothing important was said on the touchline between me and Alan Pardew, but I think it’s impossible for the referee to handle a game when every time he gave a decision against Newcastle there were complaints.
“It was an offside goal as they were interfering with Joe Hart and the referee made that call.”
City’s win was marred by a nasty-looking injury to Samir Nasri following a tackle by Mapou Yanga-Mbiwa late in the game.
Nasri left the stadium with his knee in a brace, with initial reports suggesting that the France international has suffered suspected medial ligament damage.
And Pellegrini added: “I think the tackle on Nasri should have been a red card.”
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