Victory for the Tigers would have seen them all but secure automatic promotion to the Premier League, but they rarely threatened their opponents at the KC Stadium.
"It was a bit of nerves, edginess," Bruce told Sky Sports News. "We were desperately trying too hard to do too well and getting wrapped up in the whole thing.
"It's what it is. Today the expectation got the better of us - we forgot how to play the game unfortunately.
"We knew it was a big, important game for us all. One thing we have done over past three months is handle the occasion, that's the disappointing thing."
Hull could be promoted on Saturday if Watford lose to Blackburn Rovers and Crystal Palace fail to beat Leicester City.