The dramatic 2-1 win at Valley Parade came courtesy of David Syers' 90th-minute header after Peter Vincenti had cancelled out Omar Daley's fourth-minute strike just before the break.
Victory leaves the Bantams six points clear of the relegation zone with two games remaining and Jackson said: "It was a tense afternoon, particularly after the performance at Accrington, which was simply unacceptable.
"All the fans ask is for the players to be passionate about the game and passionate about the club and they showed that.
"The players let the club down at Accrington and we needed a massive response from them and I couldn't knock them here.
Jackson added: "We deserved to win against a side that has lost only one match in 11. We created chances, particularly in the first half, and we could have been four up at half-time. The fact their keeper was named man of the match says much for our side."
Source: PA
Source: PA