Robert Snodgrass put the Canaries in front before Alexander Tettey lashed home spectacularly to seal a 2-0 win.
Marcos Alonso was sent off late on to compound a poor day for Gus Poyet's side, who remain inside the bottom three and face a tricky test at title-hunting Liverpool on Wednesday.
"We need to be ready to fight and stick together," said Bridcutt.
"We have to forget this result and move on and be ready for Liverpool on Wednesday.
"The boss has told us how disappointed he is and we know what we need to do. A positive we can take is that our next game is only a few days away."
The former Brighton man admitted the Black Cats were not expecting such a stern test at Carrow Road and was quick to offer an apology to the club's supporters.
"Of course we are disappointed with the result, it was a big game," he added.
"It turned out to be tougher than we expected and it was one of those days for us - nothing went our way and Norwich were at us from the get-go.
"I'm sorry for the fans who made the trip to Norwich, it is a long, long way from Sunderland and they deserved much more than that. Every game from now until the end of the season is massive for us - we need to keep fighting."
The win for Norwich takes them seven points clear of the bottom three with eight games remaining as manager Chris Hughton once again saw his side win when there was pressure on his position at the helm.
Scotland international Snodgrass was pleased with the vital victory but is keen to keep the momentum running into the forthcoming games with fellow strugglers Swansea and West Brom.
"It was a massive result for the boys and everyone involved in the football club," he said.
"It has been very frustrating at times but I'm delighted we have got the three points. When we have to win we produce and that is a sign of big characters.
"It is a great result for the club all round and hopefully we can build on it because that is the only way we can get out of the relegation dog-fight."
Snodgrass' opener was his third goal in six games, with the 26-year-old enjoying a spell of good performances at present - something he always believed would happen.
"A season isn't done in six months," added Snodgrass.
"I told people to be patient and to stick with and I would repay them and I feel as if I have done that."