Bradford were brought back down to earth by Oxford with a last-minute penalty four days after beating Aston Villa.
Lancashire referee Jeremy Simpson judged that right-back Stephen Darby had tripped Alfie Potter in the box and Peter Leven scored from the spot.
Leading scorer Nahki Wells had put Bradford in front after 14 minutes after a mistake by Michael Duberry, but the visitors deservedly levelled in the 19th minute when Sean Rigg scored with a right-footed shot from the edge of the penalty area.
Wilder, a former Bradford player, said: "Bradford have done unbelievably well to keep going in the cups and have had a fantastic season. Maybe there were some tired legs out there.
"It was an even first half, but I thought we completely dominated the second half and took advantage of some tired legs from Bradford's point of view.
"We deserved to beat a very good side away from home. We would have been disappointed if we didn't win the game, but we had to work extremely hard "
On the penalty, Wilder said: "Alfie Potter is dangerous in the box - maybe we deserved our fortune. Matt Duke and I are pals and we are going out together with our wives after this - I thought he kept Bradford in the game. I thought he was their man of the match - that tells its own story.
"We changed our formation from our usual 4-4-2 and I thought it worked a treat, especially in the second half."