It is the Bantams fifth loss on the bounce in all competitions and their seventh consecutive game without a win.
Prior to the game, which was won by Rhys Bennett's second-half header, manager Stuart McCall expressed plenty of confidence in his side and that results would improve.
City are only in the relegation places on goal difference and a string of wins will see them leap up the table but they are a side low on confidence and despite producing some encouraging displays in recent weeks, have nothing to show for them.
Bennett headed in for the visitors, who moved up to fourth, just before the hour as a cross evaded a host of Bradford bodies to give the unmarked central defender an easy finish.
With numerous players missing through injury, the Bantams have struggled to find their rhythm in attack. They failed to register a shot on target as Richard O'Donnell was kept busy at the other end by Carlisle.
McCall made two changes from the side that lost 2-1 to Cheltenham Town on Tuesday night.
Austin Samuels and Harry Pritchard both came off the bench in midweek but were put in from the start against Carlisle, as Kian Scales and Dyan Mottley-Henry were named as substitutes.
The Bantams had strong appeals for a penalty dismissed in the second minute after Bryce Hosannah's cross caused problems for the Carlisle defence.
It was a scrappy first 45 minutes which would have given both sides encouragement of winning the game in the second half.
Former City player Omari Patrick had a chance to put the visitors ahead but O'Donnell was down smartly to his left to keep the scores level.
That was United's biggest opportunity of the first half as Elliot Watt came closest at the other end.
A well-worked corner routine saw Connor Wood find the midfielder on the edge of the box but his first-time effort was deflected narrowly wide.
Samuels had held the ball up well for the Bantams but should have done better with an opportunity in the final stages of the opening 45.
Paudie O'Connor provided a clever knock-down for the Wolves loanee but he mistimed his shot as the ball petered out for a goal-kick.
The Bantams got off to a sloppy start in the second half and found themselves behind on 57 minutes through Bennett's solitary goal.
The lead was almost doubled after a free-kick caused a scramble in the box but the hosts managed to clear eventually.
O'Donnell was tested on a few more occasions but he stood firm to give Bradford hope of salvaging something from the contest.
However, there would be nothing for City to celebrate as they had another penalty shout waved away in stoppage time as they slipped into the relegation places.
Bradford City: O’Donnell; Wood, Richards-Everton, P. O’Connor, A. O’Connor; Cooke (French 85), Pritchard (Scales 74), Watt (Sutton 85); Samuels, Donaldson, Hosannah (Mottley-Henry 75). Unused substitutes: Hornby, Longridge, Cousin-Dawson.
Carlisle United: Farman; Hayden, Bennett, Anderton, Tanner; Devine, Mellish, Furman; Alessandra (Toure 89), Patrick, Kayode. Unused substitutes: Charters, Armer, Hunt, Reilly, Dewhurst, Riley.
Referee: G Eltringham (Durham)
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