Barrow boss Pete Wild stressed his side must stick together to secure a League Two play-off spot on the final day of the season.
The Bluebirds suffered a fifth defeat in a painful six-game winless run with a last-gasp 2-1 loss to Bradford.
It means they have to get a result when they host promoted Mansfield on Saturday.
Bobby Pointon opened the scoring with a great strike in the first half before Kian Spence levelled with a free-kick after the break.
But former on-loan Barrow forward Tyler Smith came off the bench to score a bruising stoppage-time winner against his old club.
And Wild said: “We didn’t do anything with or without the ball. We were frustrated at half-time. I told them ‘we’ve got to have a go and try to get over the line’.
“We played really well second half, had a go, came out fighting and got the goal, but it wasn’t enough.
“We were on the front foot. We kept trying to throw subs on to put impetus into the game and you get hit by a sucker punch at the end.
“We had four chances to clear the ball and that’s been the month hasn’t it. There have been key moments in game, chances and opportunities with the football and we’ve not done that.
“We weren’t getting a glove on them and we had to try and be braver, second half.
“I will never make it about them, it’s about us. We’re all a collective. We will win together and lose together and that’s how we’ve gone through the season.
“What we have to do now is just stick together and try to keep going.
“Across the last four games you have seen glimpses of us, but not enough of us across a full 90 minutes to get over the line.”
The Bantams were indebted to Sheffield-born Smith’s late winner for their fourth-straight win.
Boss Graham Alexander said: “I’m pleased that the players have once again showed character and personality to once again get a win from a game we should never have been drawing anyway.
“We were brilliant in the first half and should have been two or three up. But we weren’t and a good team like Barrow are going to come back into it and have a spell of pressure and momentum.
“Ultimately they got a goal from it. From our perspective it’s a poor one to concede going through the wall.
“Our performance became a bit flat after that. They had real quality and gained chances.
“The subs that came on halted their momentum.
“They were going for it as well and it was going to be (down to) who had that quality to score.
“To be fair to Tyler, he would have been under massive pressure in his own head, but he stuck it in the corner so fair play to him.”
