Robbie Brady struck the decisive blow just after coming off the bench in the second half of extra-time, securing Hull a scarcely-deserved 1-0 win.
"Maybe I should have brought him on 20 minutes earlier and we could have all caught our train home," manager Bruce said.
"We played them last year in the FA Cup and gave us a run for their money and they have done exactly the same.
"We knew what to expect and they're a good side. They are top of the division, full of confidence and we made a lot of changes because it is an ideal time to play the rest of the squad.
"We've made hard work of it. It is simple as that.
"We are delighted to be in the next round, but they made it very, very difficult. They played very, very well on the night. It is never, ever easy but we certainly needed to play better than we did tonight. We are aware of that.
"We've got through, that is what the cup is. But on another night we might not have.
"I don't think the goalkeepers had many saves to make but neither did theirs.
"It was one of those difficult nights for us where you're glad you're in the next round and move on."
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