Johnson and Newcastle striker Loic Remy were sent off after exchanging pushes and then squaring up head-to-head on the touchline.
"There is a bit of pushing and shoving the players have come together, there is probably just enough for the referee to send them off, but Johnson's reaction to the heads meeting, in terms that he got a headbutt when he did not, was the catalyst for them both to get sent off," said Pardew.
"It was his own fault, if he had not have done that then maybe the referee would have taken a more lenient view, but he made such a drama out of it, he should be ashamed of himself really.
"We won't appeal, because I think there was enough for Chris there, but once he done that stupid reaction, the crowd went all mad and he (referee) has got no choice really."
Pardew added: "That was the thing the game will be remembered for, when it should not have been because we had some outstanding performances, and I cannot understand how we have not won the game."
Norwich manager Chris Hughton, however, refuted Pardew's version of events.
He said: "Johnson's sending off was incredibly soft.
"I presumed something else had happened apart from what I did see, which was him push Remy in the chest - over aggressively? Not really."
Hughton added: "Bradley has not gone down on the floor. All he has done is pull his head away.
"Regards the amount of contact, I don't know, but certainly Bradley Johnson is not the type of player who would look to get someone sent off.
"My gut feeling is we will appeal, but you always have to look at it again and make the right decisions."
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