Jon Toral's deflected first-half winner handed Blues a 1-0 victory and denied Hull the chance to leapfrog Burnley at the top of the Sky Bet Championship
The Tigers are a point behind the Clarets in the race for the title and will fall behind Middlesbrough if Boro avoid defeat against Wolves on Friday
Jake Livermore and Michael Dawson hit the woodwork as the visitors dominated for long spells but could not find a leveller
Bruce said: "It's a disadvantage (for Hull) because all the others will have got a boost from it
We have 12 games to play and we have some big games
Birmingham have all the top teams here so I'm sure they'll do us a turn
"We have a lot of games coming up, a lot of points to play for and a lot of water under the bridge for everybody
"We have dominated the match really and had 20 attempts on target, but we cannot keep relying on Abel (Hernandez) to score
You couldn't say it was a bad performance."
Hull also wanted a second-half penalty after Robinson handled Hernandez's shot in the box and Bruce insisted referee Stephen Martin got it wrong.
"It's a stonewall penalty, you need the referee to do it his job and for both teams he didn't do his job all night," he said
"He knew what he was doing, Robbo, trying to put something in the way and when you see it again, it's a stonewall penalty."
Birmingham moved a point behind the top six and have kept six clean sheets in their last eight games following successive 1-0 home wins
And boss Gary Rowett revealed the victory meant he had to fulfil a promise to daughter Lily on her 16th birthday.
He said: "She was here, I was under a little bit of pressure because I obviously hadn't spent enough money on the birthday present
She said to give her a mention if we won
I'll be honest, I thought I'd probably be safe with that - making myself look an idiot - but I have to give her a little mention."
Birmingham have lost just three of their last 12 games and Rowett believes victory keeps their play-off hopes alive.
"Hull are the most complete team in the division in terms of what they've got," he said.
"At home we have been fantastic, we're making really good progress and putting in some big performances
I thought if we were to lose maybe that's our chance gone, but you end up winning
You cannot doubt your team's ability to bounce back."
Source : PA
Source: PA