The Bantams were defeated in Graham Alexander's first game at the University of Bradford Stadium, falling 2-1 to Barrow.
The visitors would take the lead in less than a minute through Dom Telford, before City levelled the encounter, thanks to Tyler Smith's equaliser.
Despite City creating some good chances in the second 45, it was Barrow who found the winner thanks to George Ray.
It was a far from ideal start to the Graham Alexander era at Valley Parade, as Barrow broke the deadlock with just 24 seconds on the clock.
In need of a response, Jamie Walker zipped in a low cross which found Tyler Smith. Smith watched his effort saved well by Paul Farman from point-blank range.
But, Smith would drag City level with an almost identical chance just after the half-hour mark. Walker was neatly found by Bobby Pointon, and he pulled back for Smith who made no mistake from inside the six-yard area.
City were forced into two substitutions in the first half after Liam Ridehalgh and then his replacement Daniel Oyegoke were both forced off with injuries, meaning Alex Gilliead slotted into the left-back spot heading into the half-time break.
The Bantams began the second half looking the most likely to snatch a second, coming back out with a renewed energy and enterprise.
Alexander's men enjoyed a lot of possession around the Barrow box but the finishing touch proved elusive. Gilliead came closest, when his effort stung the palms of Paul Farman who had to turn the ball behind.
City could not make their pressure count and, against the run of play, conceded the would-be winner in the 77th minute. After Jamie Walker had blocked the initial Barrow effort, George Ray pounced to put the visitors back ahead.
The Bantams continued to enjoy plenty of possession as the game approached its closing stages, but failed to level the game, as Barrow took all three points in West Yorkshire.
CITY: Harry Lewis, Brad Halliday (Adam Wilson 85’), Liam Ridehalgh (Daniel Oyegoke 26’ (Emmanuel Osadebe 43’)), Ash Taylor, Richie Smallwood (C) (Matt Derbyshire 84’), Jamie Walker, Andy Cook, Alex Gilliead, Tyler Smith, Sam Stubbs, Bobby Pointon. SUBS NOT USED: Colin Doyle, Matty Platt, Harry Chapman.
GOALS: Smith (33’).
BARROW: Paul Farman, George Ray, Niall Canavan (C), Kian Spence (Dean Campbell 59’), Elliot Newby, Tom White (Sam Foley 70’), Robbie Gotts, James Chester, Luca Stephenson, Dom Telford (Ben Whitfield 75’), Emile Acquah (Jamie Proctor 59’). SUBS NOT USED: Josh Lillis, Ged Garner.
GOALS: Telford (1’), Ray (77’).
ATTENDANCE: 17,247 (with 556 travelling Barrow supporters).