A fiery League Two encounter at Valley Parade was marred by an on-pitch fight after the final whistle, with referee Ian Williamson barring both managers from the dressing rooms as he took action.
Willamson dismissed three Bradford players - Andrew Davies, Luke Oliver and goalkeeper Jon McLaughlin - and Crawley duo Kyle McFadzean and Claude Davis for their part in the brawl.
All five face lengthy bans, with Bradford defender Davies set for at least five matches on the sidelines following his third red card of the season.
Bradford manager Phil Parkinson said he would fine any players shown to have thrown punches.
"The referee seems very clear in his mind what went on and that is the reason he took the action he did in the dressing rooms," he said. "Until I see the DVD it is difficult to comment, but the sendings-off leave us with lots of problems, to say the least.
"We know what Crawley bring in terms of an intimidating approach before, during and after matches. You have to make sure you don't get involved.
"Both clubs have paid a heavy price. I can't believe this has happened. I have never been in a situation before where a ref has come into the dressing room, pulled players on one side and sent them off. He wouldn't allow me in there.
"I will look at the DVD and if any of my players are guilty of throwing punches they will pay heavy fines."
Crawley manager Steve Evans also vowed to hand fines to guilty parties, but appeared to blame a Bradford player for sparking the confrontation.
"I only saw the Bradford player Andrew Davies run towards my players and throw a punch. I think it was handbags, with a lot of pushing and shoving, but it was disappointing to see.
"If people have acted out of turn they need to be dealt with.
"The fourth official confirmed to me that the Bradford boy Davies ran and punched somebody. Then there was a mass of bodies who had initially come together to shake hands.
"It is a shame because it takes away from what was an outstanding performance."