Manchester City won 2-0 at St James' Park thanks to goals from Edin Dzeko and Alvaro Negredo, but Pellegrini was disappointed with the performance of referee Mike Jones.
While Newcastle were left feeling aggrieved at the decision to disallow a goal for Cheick Tiote, Pellegrini felt Jones was actually harsh on City throughout the game.
Nasri had to be stretchered off after a tackle by Yanga-Mbiwa, for which he only received a yellow card, and Pellegrini fears his player suffered a "serious" medial ligament injury.
"The kick he made to Nasri was absolutely a red card directly," Pellegrini told Sky Sports.
"We did not have any help from the referee today. He didn't give a goal because it was absolutely offside, that is the only clear thing about which Newcastle can complain - but it was offside."
"Nasri has I think a serious injury to his knee, we will see tomorrow. I repeat it was a direct red card.
"It's his medial ligament. We will see tomorrow what has happened with him."
Pellegrini exchanged words with an angry Alan Pardew on the touchline, and explained: "He was complaining about all the decisions of the referee.
"Every time you whistle a foul he complained. I don't think that's the way to do it."
Pellegrini insisted after, however, that he had no issues with his Newcastle counterpart, saying: "Nothing, nothing. No problem."
Tiote's goal was ruled out because Yoan Gouffran was standing in an offside position and the referee felt he was interfering with play.
Pressed for his take on the incident, which angered Pardew and all the Newcastle fans, Pellegrini responded: "Of course it was absolutely offside."