Last night's goalless draw between the two sides at Carrow Road had seen both Bradley and Magpies striker Loic Remy sent off at the end.
The duo were each shown a red card by referee Chris Foy after exchanging pushes and then squaring up head-to-head on the touchline.
Pardew felt the referee had been left little option other than to dismiss both men, but slammed Johnson for his part in the melee.
"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."
Tempers had flared at the end of the first half as Scotland winger Robert Snodgrass was involved in a heated exchange with home supporters in the City Stand, which Hughton will investigate.
"Robert is a hard-working and very passionate man and somebody who is always involved in the thick of things," he said.
Newcastle, meanwhile, began life without key midfielder Yohan Cabaye, who is set for a £20million switch to Paris St Germain.
Despite the loss of Cabaye's influence, Newcastle still did more than enough to have secured victory, as they were denied by the woodwork three times.
Pardew hopes to quickly reinvest the income from Cabaye's sale.
"We looked a little bit different, but in a good way," said Pardew, who confirmed striker Luuk de Jong was set for a medical ahead of a loan move from Borussia Monchengladbach.
"This club is never going to be about one player.
"For sure Yohan Cabaye would probably get in my all-time top Newcastle team. For us he was outstanding and we wish him the very best, and I hope our fans do.
"He wanted to leave, we were honourable to him, he has got a dream move.
"We have to use that money wisely now, like we did with Andy Carroll when we brought in Yohan and a couple of others which took us forwards.
"That is how we are going to have to try to break the Champions League to use this money to good effect to make us better."
Pardew added: "I was on the phone to the powers-that-be to say 'let's get moving and see what we can get'
"We have one or two targets which we had earmarked if he went and we are chasing those down."