"It should have been a red card for the tackle by Yanga-Mbiwa on Samir Nasri," City manager Pellegrini told reporters. "A direct red card - we didn't have any extra help from the referee today.
"Nasri has a serious injury with his knee - it was directly a red card. Maybe it's medial ligaments. We'll see tomorrow what happens with him."
The 26-year-old French international, who should be named in France's World Cup squad this year, was writhing in pain on the pitch before being carried off on a stretcher after a six-minute stoppage in play as he was treated.
He left the ground on the team coach with his knee in a brace and his immediate future in doubt after the hack which earned Yanga-Mbiwa only a yellow card.
There was better injury news for City later on Sunday as striker Sergio Aguero announced that he could make his return from injury in Wednesday's FA Cup third-round replay with Blackburn.
Aguero, 25, returned to training this week after recovering from a calf injury that has ruled him out since the 6-3 Premier League win over Arsenal on December 14.
The prolific forward, who has scored 19 times in 20 appearances before his lay-off, is targeting a return in midweek, with manager Manuel Pellegrini having hinted that Aguero could make a return against Cardiff on Saturday.
"I'll be ready for action this week," Aguero said on his official website.
"My injury is improving slowly. Recovery's going very well. I'm back to sprinting on the field and moving the ball around.
"I'll be fully recovered by the Cardiff game and depending on how the week's training goes I may be able to show up for a few minutes on the second leg against Blackburn for the FA Cup."
Aguero is keen to make a return to action with City top of the Premier League standings, and still in the FA Cup, League Cup and Champions League.
"We are putting up challenge in every competition this year, the striker said. "Then the World Cup is coming up and I hope to keep my form and the level of my game when it arrives.
"Manuel wants us to have possession, he wants defence to keep the pressure up. Since he arrived, he's been working on improvement and I think the team is shaping up already.
"I'm happy with my tally and my performance. Goals I especially like because they win games and most of them decided a match, so that's what makes me happy."