The only goal of the game came in the eighth minute when Kyel Reid's free-kick found James Hanson at the far post and he headed the ball down for Garry Thompson to fire home from five yards.
Ainsworth, who came on as a substitute in the second half, said: "We were second best for a lot of the time, but our keeper didn't have to make a save after the first five minutes.
"Set plays are so important in this division. What disappoints me is that we didn't organise properly and let a goal in. The game was won and lost in the first five minutes.
"Physically we were a little bit short short, but it was a very workmanlike performance from Bradford and fair play to Phil Parkinson, he has done well.
"Bradford were a wounded animal after Saturday and I knew Phil Parkinson wouldn't stand for that."
