Tigers boss Bruce named a completely different side to the one that secured their first Premier League win of the season against Norwich at the weekend and he saw Orient dominate for large periods.
However, Robbie Brady struck the decisive blow just after coming off the bench in the second half of extra-time and Bruce was a relieved man afterwards.
"Maybe I should have brought him on 20 minutes earlier and we could have all caught our train home," 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."
The poor performance of Hull's periphery players in east London will be of concern to Bruce as he looks ahead to a tough season back in the top flight.
"You don't want to undermine it, of course you don't," he said of the 11 changes. "You want to give your squad a chance because the difficulty of playing in the Premier League is that it makes this the ideal opportunity to play the squad.
"They've played this evening but we all know the Premier League has got to be the priority.
"We are new in there and we've got to make sure we do everything we possibly can to stay up, keep the squad intact.
"The more games you play, the more chance you have of getting an injury to your big players and that is always in the back of your mind.
"We're delighted we got there, but it wasn't a great performance. Orient played very well on the night."
It was Orient's first defeat of the season, having won five matches on the bounce heading into the second-round tie.
"I just had a sandwich with Steve and he was saying that we deserved a little bit more than what we got," manager Russell Slade said.
"We just don't seem to be able to get one over on them in some very, very tight games, do we?
"I am very proud of the performance tonight. It was a very good, strong performance.
"I thought there were some nice passages of play, we put them under a lot of pressure whether it was from a corner, throw-in or open play.
"I was pleased, I can't hide that. I couldn't have asked for much more from them, they gave me everything."