Phil Parkinson admitted it was tough to take after Wrexham suffered their third consecutive league defeat.
Andy Cook scored Bradford’s late winner just minutes after his penalty had been saved by Arthur Okonkwo.
But manager Parkinson felt his team had done more than enough to take the points as their promotion hopes took another hit.
He said: “It hurts. We dominated the game, particularly in the first half when we were excellent.
“We set out to do everything we wanted to against a 3-4-3 system, moved the ball well, got in some good positions and just couldn’t find the moment.
“The way we played probably justified us coming in one or two ahead. That was probably as good a first-half performance as we’ve put in for a while.
“We know we’re in a period where it’s not going our way but the lads have given us absolutely everything today.
“We just couldn’t find the moment to unlock the door. But it was certainly not through lack of effort.
“We were very much on the front foot all over the pitch but football is about putting the ball in the back of the net. It’s very rare for us at home.
“When you’ve had a few defeats and things are going against you, that can happen.
“We deserved to win the game but one big moment proved decisive.”
Cook claimed his 14th goal of the season, heading home from close range after Okonkwo had blocked his initial effort.
It was a first win in nine league games for the Bantams – and second at the Racecourse Ground for manager Graham Alexander, who had beaten Wrexham with MK Dons on the opening day of the season.
Alexander said: “I can’t speak highly enough about my players.
“Wrexham are always going to have moments in games because they’ve got an array of talent and their belief is massive from their two-and-a-half year run.
“I feel defensively we’ve been really strong, really disciplined and structured. It’s just taking the moments in front of goal that has let us down.
“That’s the whole team, not just the forwards, it’s midfielders getting in there, defenders from set-pieces and things like that.
“We all have to take responsibility for those opportunities. If we had done that, I think we would have won many more games which we deserve.
“We are where we are. We’ve won a big fixture today for us and hopefully it will give the players and supporters the belief that there’s still something there worth fighting for.
“There was a freshness about us because we knew we had to work exceptionally hard. They are a very good team with an unbelievable home record.”