The Black Cats made nine changes from the team that beat Blackburn on Saturday, but it did not matter as Teemu Tainio set the ball rolling for the Premier League club after 26 minutes, Andy Reid chipped in a second and he made it 3-0 before half-time.
Norwich midfielder Wes Hoolahan reduced the deficit just after the hour, only for Owain Tudur-Jones to deflect a corner into his own net.
Norwich finished the match with nine men after defender Michael Spillane was sent off for a professional foul on Fraizer Campbell and goalkeeper Ben Alnwick went off after suffering a cut to his face.
"We made some changes, and it was good to see the ones who needed a game," said Bruce, who revealed striker Campbell had suffered no worrying injuries from his clash with Alnwick.
"All of the lads have come to the party in some way or another and asked a few questions. I can only play 11, but you could see tonight there are five or six knocking on the door, big style."
Sunderland hope to secure the season-long loan signing of Lyon defender John Mensa, and are also closing in on highly-rated 21-year-old Egyptian Ahmed Al-Muhammadi.
"John Mensa is waiting for his visa to be stamped, and we hope to be able to bring him to the club in the next few days," said Bruce.
Dubliner Reid, 27, underwent a rigorous fitness regime in the summer to cut down his notoriously excessive weight and Bruce praised the former Tottenham and Charlton man's dedication to the cause.
"I do not think anyone has questioned his ability, but the one thing which has been levelled at him is his physical condition," said Bruce, who was part of the Norwich team which won the Milk Cup back in 1985.
"He has now lost something like nine kilograms, 22 millimetres of body fat, which has taken him down to what you have seen today. He has always been blessed with ability, and now has got himself in a condition which you have to be – I think the penny has dropped that you have to be that way to play in the Premier League."
Bruce added: "Fair play to him, he is the one who has done it, I am not going to take any credit for that. Over the summer, he has worked hard and watched what he has put in his mouth. We all know what to do, but it is very difficult."
Norwich manager Paul Lambert, meanwhile, felt there were some positives to take from the match. "We started really well, and had some good chances," said the Scot, appointed following the dismissal of Bryan Gunn.
"However, when you make individual errors, especially against calibre like that, you will get punished.
"There were some positives to come out of it, and the negatives, well I have already seen them."
Lambert, whose former side Colchester thrashed Norwich 7-1 at Carrow Road on the opening day of the season, added: "It is not about a magic wand, it is to try to get the club up the league."