Victory in midweek would have lifted the Bantams to within a single point of seventh position, but a below-par performance at Valley Parade ensured that they finished the night empty-handed.
And, with a big Yorkshire derby at Harrogate Town up next, joint-manager Conor Sellars insists that his players cannot afford to dwell on their loss to the Red Devils.
"It's important to put that disappointment behind us," he said.
"Initially it hurt, that frustration was clear for everybody to see. Me and Mark [Trueman] felt the same way and obviously we weren't too happy with the performance, as well as the players, because they look at themselves and look at each other and for whatever reason we didn't perform well enough in quite a few areas.
"But, we can't just dwell on it. Harrogate Town is the next game, we've got to go and put a performance in and see what happens."
Avenging October's 1-0 home reverse at the hands of League Two newcomers Harrogate and bagging all three points would certainly bring City back into contention in terms of the battle for a top-seven finish.
And, although he admits that his team are probably outsiders to end the campaign in a play-off berth, Sellars says that the Bantams still feel they can do it.
"I think we do believe, collectively," he added.
"We want to win every game. We have had runs in the past where we've put together some really good results, so I think we are positive and we are hoping to get a good response [to the Crawley defeat] and a good end to the season.
"If we're there [in the play-offs] at the end then that's a huge bonus and a massive congratulations to the players and everybody at the club.
"Is it possible? Yes. Is it likely to happen? Probably not, but we'll do our best to try and make it happen."