The champions, beaten at Sunderland on Boxing Day, were off to a flying start when they went 2-0 up inside four minutes after Edin Dzeko's quick brace.
Norwich reduced the deficit through Anthony Pilkington's deflected free-kick before Nasri was shown a red card by referee Mike Jones after 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.
Mancini - who is already facing a Football Association probe for comments after the Sunderland game that referee Kevin Friend had "ate too much for Christmas" - felt City were hard done by and will appeal against what is set to be a three-match ban.
Things got ugly again just before the break when Bassong upended Nasri on the far touchline.
The duo squared up face-to-face, with Nasri pushing his head into the Norwich defender - which on consultation with the assistant referee resulted in a red card for the France midfielder and a caution for Bassong.
Mancini lamented: "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.
"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."