The Bantams enjoyed a dream run to February's Wembley final thanks to victories over Wigan, Arsenal and Aston Villa, but there will be no repeat after a double from James Vaughan gave the Terriers victory, despite Nahki Wells' late strike.
Championship Middlesbrough suffered a shock defeat as they were beaten 2-1 by League Two Accrington at the Riverside Stadium.
Ipswich were another second-tier side to be dumped out by lower-league opposition as they fell to a 2-0 defeat at Stevenage.
A penalty from Filipe Morais early in the second half put Stevenage ahead, with Jordan Burrow sealing the win.
Rotherham upset local rivals Sheffield Wednesday with a 2-1 win. Ben Pringle put the Millers ahead before Rhys McCable levelled for the visitors.
Lee Frecklington put the hosts back in front before Wednesday substitute Jermaine Johnson was sent off for a headbutt on Pringle.
Watford were comfortable 3-1 winners at Bristol Rovers. A brace from Sean Murray and a Gabriele Angella strike put the Hornets in control before Eliot Richards pulled one back for Rovers.