Ryan Bennett headed the winner three minutes from time at Carrow Road on Saturday, meeting Robert Snodgrass' corner to consign Hull to a fourth defeat in their last five Premier League games and earn Norwich their first win seven league matches.
To make matters worse for Hull, Tom Huddlestone was sent off for a second bookable offence right at the end and will now miss Saturday's trip to Southend United in the fourth round of the FA Cup.
Bruce, who said he had no complaints over the red card, could not hide his frustration at the manner of how the winning goal came about.
"Unfortunately what's cost us is (Liam) Rosenior, who was arguably our best player, has come off the post to pick somebody up," he said.
"The lad who he's gone to pick up goes and heads it and he's not on the post. Yannick Sagbo was picking up their centre half (Bennett) but then he came off.
"We tried to get onto Nikica Jelavic to pick him up, but unfortunately that communication didn't happen. And Liam who usually stands on the post has to come and pick him up and unfortunately he's got caught underneath it and where he heads it is where Liam should be, so it's a touch disappointing.
"Overall, second half we were disappointed in the way we handled the ball. When you do that and don't play as well as you'd like to, to come away with a point would have been terrific, however. it wasn't to be."
The closest Hull came was when Jelavic, signed in the week from Everton, struck the post in the second minute, a miss that left Bruce to further lament his side's luck.
"He's done everything right," he said.
"His connection is right, it's on his left foot and he's struck it really, really well and I'm expecting it to nestle in the back of the net.
"But it's hit the post and missed by two inches, so on another day it would have nestled into the net and what a start that would have been for the lad."
