The Tigers shipped two goals in the final three minutes to crash out of the Capital One Cup at The Hawthorns.
The Baggies' late show - thanks to goals from Gareth McAuley and Saido Berahino - won it 3-2 to clinch a trip to Bournemouth in the last 16.
It was the fourth time Hull have blown a lead this season after tossing away six points in the Barclays Premier League to Stoke, West Ham and Newcastle.
They lost a 2-0 lead at St James' Park on Saturday and Bruce is frustrated with the Tigers' inability to hold on.
He said: "We could have had a wonderful start but it's cost us
The one thing which enabled us to get out of the Championship was the ability to defend as a team.
"We didn't clear a corner for the second goal and there's frustration and disappointment etched over every one of us.
"We are really close to having a really good team and a really good squad
It's frustrating, as you can imagine.
"With three minutes left you are thinking 'I'm going to leave this alone'
We were so comfortable you are thinking it's going to be us to score another
The third one is a lack of concentration and we were probably in a state of shock after what happened."
Robbie Brady and Tom Ince had given Hull a 2-1 lead after Brown Ideye opened the scoring for the hosts.
It was his first goal for the club after a £10million summer move from Dynamo Kiev but the Baggies are sweating on his fitness after he injured his ankle scoring and had to come off.
Head coach Alan Irvine said: "Brown has rocked his ankle when he scored so it was a bitter-sweet moment.
"On one hand he scored, on the other he had to go off
He'll be happier because the pressure goes on strikers when they don't score.
"Strikers are judged on their goals and everyone is desperate for him to get them.
"He shows in training he's a good finisher and it was a shame he had to go off but I don't think it's too bad."
The victory built on the Baggies' first league win of the season, Sunday's 1-0 victory at Tottenham.
Irvine admitted he felt they were out but praised their fightback.
"I didn't think it was going to come but when we got one I thought 'extra time again' but fortunately we finished a bit earlier," he said.
"Hull's first goal was self-inflicted, I was disappointed with the nature of it and bitterly disappointed to go in at 1-1 because we shouldn't have done.
"To lose the second goal made it more difficult but we kept going and creating chances."
Source : PA
Source: PA