Hull stretched their lead in the Sky Bet Championship table to two points over Middlesbrough and Brighton moved up one place to third following the draw.
Sam Clucas was closest to breaking the deadlock with a late shot which Brighton goalkeeper David Stockdale tipped onto the crossbar and Bruce conceded his side looked nervous.
Brighton played with five in midfield and Bruce had hoped his side would do more with the space they were afforded by Chris Hughton's game plan.
"I thought he might go with just one striker," said Bruce.
"To leave out (Bobby) Zamora, when a team does that - and we've seen it so often here - you need to take care of the ball better than we did today
We got a bit nervous and a bit edgy with the ball.
"Fair play to Brighton, they have come and worked very hard and frustrated us.
"When you get a point away from home you are going to be happy with that
They have come with a game plan and it's worked very well.
"We didn't play well enough tonight and that's going to happen
We take the point and move on."
In an uninspiring match, the only time Brighton worked home keeper Allan McGregor was in the first half when he beat away a shot straight at him by Jamie Murphy with nearly half an hour gone.
Hull midfielder Tom Huddlestone wasted a free-kick when he fired well over but went closer when he shot narrowly wide later in the first period.
Despite that Hull still had the best chance of the game when Clucas came closest to scoring late in the game.
His rising shot was tipped on to the bar at full stretch by visiting keeper Stockdale.
Brighton manager Hughton felt his change of formation, bringing in Inigo Calderon and Steve Sidwell, worked.
Hughton said: "We played a different system
I was pleased in Calderon and Sidwell, I was really pleased with both of them.
"I think with the form that Hull are in at the moment, you've only got to look at the side and at their bench
At any stage of the season against these it's a good result
I think on the balance of play and the chances, I think we deserved it.
"You want to make it a tight game and the chances are going to be minimal."
Hughton praised Stockdale, who had little to do in the game but still came up with a fine save to deny Clucas.
"That's what he's done ever so well for us
His concentration levels have been very good," added the Brighton manager.
Source : PA
Source: PA