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 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.
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."
Mancini continued: "I am disappointed with Samir, and he will pay his fine, but the decision was not correct.
"Samir did a mistake, okay, but after why when the other player did the same thing, does he send off only one?
"There are two rules for different teams, and I hate this in football and cannot accept this.
"In life, there is only one rule for everyone.
"This season, I have seen things which are not good.
"For the referees, this is the most easiest thing to do, but I do not want to talk about the referees too much, because I said last time that they had a big lunch for Christmas, and I don't know what [will happen]."
City have now won three out of their last four Premier League games, but still trail leaders Manchester United by seven points.
Mancini was just happy to get a victory, which was made harder by some poor defending as all of Norwich's goals came from set-plays.
"I am delighted with the result and the performance," the City boss said.
"In the first few minutes, we played some fantastic football and scored two goals, but after the sending off it was difficult, however, we fought well."
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, remained positive despite a second home loss in a week, after Chelsea ran out 1-0 winners in Norfolk on Boxing Day.
"Manchester City showed why they spend the amount of money they do for the offensive players they have, but you cant be 2-0 down so early on and expect to have a good day," Hughton said.
"However, we displayed great character and certainly at 4-3 it seemed it might be going our way, but again they showed real good quality.
"I cannot fault the endeavour of the players we have got, so now we will look to go again."
Hughton could empathise with Mancini's complaints on the refereeing.
He said: "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."