Leading 1-0 from the first leg, City went behind in the 21st minute when Brad Halliday diverted the ball into his own net with the scoreline remaining the same in 90 minutes – level on aggregate.

The Cumbrians added a second courtesy of a Callum Guy drive on 98 minutes, but substitute Matt Derbyshire levelled the tie with a close-range strike eight minutes later.

But City’s defence switched off fatally on 113 minutes with the tie-breaking moment heading in the Cumbrians’ direction when Ben Barclay beat Harry Lewis to head home following Owen Moxon’s cross to book Carlisle a final date against Stockport on May 28 after a 3-2 aggregate win.

City will now start a fifth successive season in League Two in August.

Hughes said: “It is disappointing and it is not the way we wanted the season to end. But it is a season of progress and one I have really enjoyed. There have been great moments and moments where we have hurt ourselves. But the club is a in a good place now and that will give us the base to go this year.

"People will be disappointed because the expectation was that we'd get out of this league and we haven't done that and the expectation was not fulfilled.”

Reflecting on a see-saw game in Cumbria, he continued: "We got back into a situation where we obviously got back in the game and the tie was still up for grabs and we just made an error when the ball came into the box and we had enough numbers there and we should have done better.

"We should have done better with all the goals in fairness, but that can happen. There were balls that we didn't deal with correctly and you need that luck to make sure they go the wrong side of the post because if luck is against you, they go inside of the post and unfortunately that is what happened to us.

"We got back into the game clearly. It was a difficult game and it is not easy to play Carlisle, they hit it long and they complete for every ball and things drop in midfield areas and it gets hooked on and it gets very difficult to get a foothold in the game.

"I thought we did that towards the end of the game (in the first half) and started to get a grip so that we had the better of the game in the second half. But the way we conceded the goals was the story of the day really.

"If you look at the timings of the goals and the one we scored, it's illustrated that it's difficult to play when you are tired and you don't quite think as clearly as you should do and that is what happens when you make mistakes.

"Your decision-making is affected by the effort you put into the game and you could see the effort from both sides. Teams were making mistakes and mistiming clearances and we benefitted from that for our goal.

"They just had a moment at the death which we could have dealt with better and should have done. We'd have taken chances with the pens or maybe created something at the end for ourselves.”

Mark Hughes insists Bradford City can reflect on a season of progress despite painful play-off loss at Carlisle United