After Edin Dzeko notched a brace inside four minutes, Norwich reduced the deficit through Anthony Pilkington's deflected free-kick, before Nasri was shown a red card by referee Mike Jones on 44 minutes for putting his head into the face of Sebastien Bassong.
Although the decision did not eventually cost City as Sergio Aguero and an own-goal from Norwich keeper Mark Bunn eventually saw off the spirited Canaries, the Italian was left less than impressed by the whole incident, saying it was "not a good decision".
"Both players came forward with their heads, so if you are going to send off one, then you have to send off both, not only Samir," Mancini said.
"Samir said he touched his head, okay, but the other player has done the same. The linesman has a big responsibility also, because it was not a good decision, it is incredible.
"You want to send off both players? Then, okay, the referee was there, he saw everything. The linesman was behind [the players], he could not see. We will appeal, sure."
Norwich, meanwhile, have now lost three Premier League games in a row, having been on an unbeaten 10-match run before Christmas. Canaries boss Chris Hughton, though, is remaining positive.
"We displayed great character and certainly at 4-3 it seemed it might be going our way, but they showed real good quality," he said. "I cannot fault the endeavour of the players we have got, so now we will look to go again."
Meanwhile, Hughton could empathise with Mancini's complaints on the refereeing, adding: "In the build-up to their second goal, there was a foul by Vincent Kompany in midfield, which was disappointing.
"On the sending off, there was certainly a coming together of heads and some movement, now whether that was enough for a sending off... if the referee has given it for that reason, was it a bit harsh? Probably yes."
Source: PA
Source: PA