Alvaro Negredo - strongly linked with Hull four years ago - came off the bench to break the deadlock in the 64th minute and Yaya Toure made the result certain with a late free-kick.
For the Tigers, Sone Aluko squandered a glorious chance to open the scoring in the early stages and Danny Graham had a good strike ruled out for offside.
Bruce said: "We are going to be rightly disappointed with the scoreline but I am immensely pleased with the way we played and the way we took them on. We couldn't have asked for anything more.
"Our Achilles heel, even last year in the Championship, was can we score enough.
"You can see why we have come out of the Championship with the football we have played, but we need to score.
"We have had a big chance. Sone would have capped a wonderful performance from him if he stuck it away.
"Then the linesman gave an offside, which is right, but it was two inches offside, which I thought these days is supposed to go with the attacker.
"When you realised how close it is, it is a big call. You need that little bit of luck when you come here but it wasn't to be."