The midfielder was given his marching orders just before half-time after appearing to headbutt Canaries defender Sebastien Bassong following a strong tackle by the latter.
Nasri will now serve a three-match ban – unless the club protest the red card - which includes the trip to former side Arsenal on January 13, but Mancini was adamant the Frenchman was innocent.
"It was not a red card. It was not a red card," he told Sky Sports News. "I can't understand why the linesman told the referee it was a red card. Samir did nothing.
"It changed the game. We would have won the game no problem, but with 10 players it was difficult. Norwich is a good team.
"But today we showed that we are there for the title because we [showed] fight.”
City were two goals to the good after just four minutes thanks to a double from Edin Dzeko, but a resilient Norwich side battled throughout before eventually succumbing to a 4-3 defeat.
Mancini was pleased to get back to winning ways after the 1-0 loss to Sunderland, but reiterated his belief his team deserved all three points on Boxing Day before dismissing the seven-point gap between themselves and title rivals Manchester United.
He continued: "We played well and deserved to win [against Sunderland], we just failed to score. It is like that every year at Sunderland, we have 21, 22, 23 chances to score, and we don't score. But, that is in the past. We won today.
"It is not important to look at the table. We just need to work, win and win many games in the row. Then we can look at the table in February."