Daniel Agger headed Liverpool into the lead with nine first-half minutes remaining, before Luis Suarez scored his 20th Premier League goal of the season after the break.
Suarez curled an excellent free-kick past Hull goalkeeper Allan McGregor to seal the win, as the lethargic visitors had no response.
"You could see towards the end, we were game enough to keep trying but you could see a lot of tired bodies from our team," Bruce said.
"The third game in six days was a bit too much for us. The disappointing thing for me is that the game is settled by two set-pieces, a corner and then Suarez has produced something extraordinary again.
"And that has made the game so comfortable for them in the end.
"It was a big, big ask for us today and to get a result for a club like ours, you've got to be right at it, you need to be fresh."
Bruce insisted that was not an excuse though, and that Liverpool completely deserved their three points.
He added: "Sometimes you have to say you were beaten by the better team. We were today -as simple as that."
