Town defenders Pablo Mills and Claude Davis were both sent off as a melee erupted whilst the two teams shook hands. Three Bantams players were also dismissed.
"Regarding the unfortunate events which took place at yesterday's (Tuesday) game with Bradford City after the final whistle was blown, Crawley Town cannot make any further comment until the club has had an opportunity to view the video footage in detail," a club statement read.
"Following a full internal investigation, the club will decide whether there is the need for further disciplinary action in addition to that already taken by the Football Association, or to appeal against the suspensions handed out."
Manager Steve Evans has already promised that `people [who] have acted out of turn need to be dealt with,' and will no doubt be a major part in the investigation.
Crawley moved back into the automatic promotion places as Gary Alexander and Leon Clarke scored to give them a 2-1 victory.