QPR manager Neil Warnock and Joey Barton said the officials were "conned" when the Rangers captain was sent off in the .
Barton was dismissed after an off-the-ball incident with Bradley Johnson.
"The assistant referee has guessed, if I'm honest," Warnock told BBC Sport. "Who says cheats don't prosper? Bradley has conned him."
Barton added on Twitter: "Hopefully [the] ref sees it retrospectively and sees he's been conned."
Norwich were quick to capitalise on Barton's dismissal as Anthony Pilkington scored just before half-time, with Steve Morison clinching a late winner.
"It is difficult," said Warnock. "Their heads are together but I don't think Joey Barton would have gone down if it had been the other way round and that is the difference.
"It doesn't surprise me that Bradley Johnson went down. I loved the bit where he held his mouth as if he headbutted him - you don't expect that extra."
Barton, who had given Rangers an 11th-minute lead, said the officials told him at half-time that they "never saw" the incident with Johnson.
"[I] feel for the officials; they've been conned. I was pulled back first, then kicked second," Barton tweeted after being sent off for the first time in his QPR career.
"Linesman definitely never saw it, all he saw was Johnson's reaction. My head doesn't move forward at all. Ridiculous decision. [I've] seen 25 replays."
Barton, then at Newcastle, was involved in another controversial incident on the opening day of the season, when he admitted "going down easily" in an altercation which led to Arsenal forward Gervinho being shown a straight red card.
Supporting the Rangers captain for his role in the latest incident, Warnock called for Johnson to be punished, but was not optimistic that Barton's red card would be overturned if QPR decided to appeal.
"He has not been headbutted at all, not in a million years," said the Rangers manager as he reflected on Johnson's reaction. "The movement of him going backwards has conned the referee.
"To go back like he did was a disgrace. It's getting a fellow pro sent off. I think he should be [punished].
"We will have to look and see what the referee says in his report and if there are any other angles, but from every one I have seen, I don't see a headbutt.
"We will have to decide later. I have not got any confidence in the appeals procedure. I am not optimistic."