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.
Head coach Dean Smith complained about a congested fixture schedule which had seen his depleted squad without the likes of Lasse Vibe and Alan Judge through injury.
He said: "We played three games in March and eight in April
The Premier League and FA Cup seem to take precedence over the Championship now.
"Hull City can rotate their squad and they had fresher legs tonight.
"We were organised behind the ball and made it difficult for them
We got caught out by a big diagonal ball and Harlee has put it in his own net.
"It was very difficult to get back in the game after then
The second goal just on half-time made it too much of a mountain to climb in the second half.
"I've got some bodies at home who are feeling a bit tired
It's too many games in too short a period."
Source : PA
Source: PA