Birmingham manager Lee Bowyer felt Hull’s controversial opening goal was “not acceptable” after his side lost 2-0 at the MKM Stadium.
Ryan Longman appeared to have taken the ball out of play on the left flank before crossing for George Honeyman to score from close range after 17 minutes.
But linesman Akil Howson and referee Tony Harrington allowed the goal to stand – much to Bowyer’s dismay.
Bowyer, who was shown a yellow card at half-time for his protestations, later called for VAR to be introduced in the Sky Bet Championship:
Bowyer said: “The rewards of VAR are massive. They (officials) need help. They (Hull) have been given a goal head start for nothing. It’s not acceptable.
“We want the right decisions. It’s the worst and hardest job (being an official). Help them – they’re human.
“I like the linesman, but he’s made a mistake. And because I’m saying the truth (at half-time), they don’t like it.
“They (officials) have to get punished. As a group they have to be punished, but it never happens – it’s crazy.”
Birmingham were second best once Honeyman scored and were then reduced to 10 men after Gary Gardner was sent off for an alleged headbutt on Josh Magennis after 43 minutes.
Hull later put the game to bed when Mallik Wilks headed home Keane Lewis-Potter’s smart back-post cross in the second half.
Bowyer said: “They got given a one-goal head start and probably the only people that didn’t think the ball went out was the officials.
“I still think we’d go on and win the game, but then Gaz (Gardner) gets sent off and that’s it. He’s let everybody down and we now lose him for four games.
“He’s played the game long enough and he’s got punished for it. I won’t defend him.
“You can’t do that. He’ll get punished and rightly so. We’ve got no defenders and it’s going to be tough for us. But we’ll have to adapt and find a way to win games.
“At least the player kept going until the end.”
Hull, now outside the Championship relegation zone following back-to-back wins, played well and were good value for three points.
Head coach Grant McCann said: “It’s been a pleasing day. It was a good performance from start to finish.
“It’s been difficult, with all the players that are unavailable, but for large parts of the game we were in control.
“It’s been a tough few weeks – we had all the fit defenders available that we could play here.”
On the first goal, McCann said: “You make your own luck. We got a wee bit of a break with that decision, but the most important thing was the performance.
“We don’t want to be where we are in the table, but there’s a long way to go. The players are getting better and better and I can see that.”
Hull are reportedly close to a £30million takeover from Turkish businessman Acun Ilicali, but McCann said: “There’s been a lot of talk about it.
“I can’t control that. All I can do is control the players and the team. All I can do is focus on the group. We can’t control any of it. My only focus is on the team.
“We’re trying our best and trying to get better. We’re all still learning in this division.
“All I can do is focus on everyday life at Hull City. Overall, a really good team performance.”
