Referee Steve Bratt admitted he blundered over the game-winning corner as City stumbled in their last warm-up for Wembley.
Bottom club Wimbledon’s last-gasp victory left a sour taste to begin the build-up to Sunday’s Capital One Cup showpiece with Swansea.
Gary Jones revealed that the official had apologised for getting it wrong over the corner which led to Gary Alexander’s winning header.
Jones said: “It was never a corner. The linesman gave it from the other side of the pitch – there must have been ten bodies in the way.
“I asked the referee at the end of the game and he said he’d made a mistake.
“That doesn’t cushion the blow after losing in the last minute. It was a massive error from the referee but we’ve still got to defend it and then we get a point.”
City looked to be cruising towards back-to-back away wins once Garry Thompson fired them in front. But unlike at Wycombe, they were unable to find a second goal – and were stunned by a late one-two.
Skipper Jones said: “I don’t know how we lost that game. The second half was the most one-sided I’ve played in all season.
“That was probably our best away performance. We were totally in control of the game.
“Thommo scored a great goal and maybe should have scored a second but the pitch had a lot to do with it. The ball wouldn’t sit down for him.
“It’s a massive disappointment because we were in total control.”
Defeat leaves the Bantams still seven points adrift of the League Two play-offs, with a game in hand as they switch focus to the cup final.
Jones said: “Football’s like that. It kicks you when you don’t expect it.
“It would have been brilliant going to Wembley on the back of two wins. That’s not the case.
“But we’ve got to pick ourselves up. There’s no point in dwelling on it now and we’ve got a great week coming up.”
Phil Parkinson denied that Wimbledon’s first home win since October was down to City thinking of Wembley.
The City chief said: “People might say that but it’s totally inaccurate. I thought the lads were magnificent.
“We just needed that extra goal to kill them off but couldn’t get it. I thought they were there for the taking and we should be talking about three points.
“I just felt so confident. I couldn’t see them having a shot, let alone scoring a goal – and they scored two.
“Their corner looked like a goal kick to me. All the players started walking towards the halfway line then the ref appeared to change his mind.
“The fourth official said to him on his mic that he thought he was wrong. But we’ve still conceded two sloppy goals.”
Parkinson also confirmed that Andrew Davies was “fine” after the defender was troubled by a calf spasm in the closing minutes.