With Hull unable to reach the automatic promotion spots in the Sky Bet Championship fans called for unpopular owner Allam, who is suffering with an unspecified illness, to quit the KC Stadium.
His unsuccessful bid to change the team’s name and the introduction of a membership scheme for next season has led to protests, with fans showing red cards before kick-off and also calling for him to sell up during the game.
Bruce said: “The one thing that disappoints me is all the protests and red cards. At the end of the day the chairman, at the moment, is not well at all and this will not help him.
“He’s put £70million of his own money into the club. He’s obviously upset and disappointed but just be careful what you wish for.
“I can’t see many more people round here who will bail out Hull. When I first met him he bought the club for the community. He has built cancer hospitals.
“It’s been the best five years in the history of the club and it will be remembered for the membership scheme and the name change.”
Bruce admitted some of the seven players he had brought into the starting line-up had given him food for thought ahead of the play-offs.
“Two or three of the performances, it’s given me a headache with what I’m thinking about,” he said.
Hull took the lead just after the half-hour when Andy Robertson raced down the left and squared the ball hard and low and Harlee Dean could only turn it into his own net.
The home side should have gone further in front but Adama Diomande’s penalty was saved by David Button.
Hull made it 2-0 in first-half stoppage time as Mo Diame took two attempts to score from Harry Maguire’s low cross on the right.
Brentford rarely threatened, Marco Djuricin shooting wide in the first half and Sam Saunders hitting a free-kick narrowly off target in the closing moments.