The Bantams fell to a 1-0 defeat to Barrow at the Progression Solicitors Stadium.
Having fallen behind in the first half, Stuart McCall's side were then reduced to 10 men and proved unable to provide a response after the break.
The Bluebirds scored the only goal of the Sky Bet League Two fixture in the 18th minute - through Connor Brown.
After being teed up by Jason Taylor, the full-back’s low effort beat Richard O’Donnell down to his left.
In the 30th minute, skipper O’Donnell was forced into a fine save to deny Dior Angus from doubling Barrow’s lead.
The Bantams went into the half-time break both a goal and a man down, after Levi Sutton was dismissed for lunge on Taylor eight minutes before the break.
The visitors started the second half on the front foot but failed to capitalise with any clear-cut chances.
In the 60th minute, Clayton Donaldson worked himself into a good position at the edge of the box but snatched his shot which trickled past the near post.
Angus forced O’Donnell into a good low one-on-one save - after the attacker beat Finn Cousin-Dawson and shot towards goal from inside the area.
Despite making a number of attacking changes in the later stages, the Bantams proved unable to get on the scoresheet and take anything home from Cumbria.
BARROW: Joel Dixon; Connor Brown, Patrick Brough, Jason Taylor, Matt Platt, Sam Hird (c), Mike Jones, Dior Angus (Jayden Reid 73’), Harrison Biggins (Chris Taylor 73’), Brad Barry, Luke James. Subs (not used): Scott Moloney, Yoan Zouma, Scott Wilson, Dimitri Sea.
GOALS: Brown (18').
CITY: Richard O’Donnell (c), Bryce Hosannah, Paudie O’Connor, Anthony O’Connor, Reece Staunton, Connor Wood; Finn Cousin-Dawson (Elliot Watt 73’), Levi Sutton, Callum Cooke; Austin Samuels (Dylan Mottley-Henry 63’), Clayton Donaldson. Subs (not used): Sam Hornby, Ben Richards-Everton, Harry Pritchard, Tyler French, Billy Clarke.
REFEREE: Benjamin Speedie