The NRL admits it was unacceptable for play to continue while Nene Macdonald was down with a fractured ankle and dropped the referees in charge of the game.
The governing body came under fire after play continued for almost a minute while two North Queensland players were injured against Melbourne on Friday.
NRL head of elite football Graham Annesley on Monday confirmed whistleblowers Grant Atkins and Gavin Badger had been demoted.
"It's important for me to say that as an administration, we didn't find that acceptable, that it took as long as it did for the game to stop," Annesley said.
"There were any number of eyes across that through the on-field officials, and the match-day coach who was also watching the game.
"We felt there was ample opportunity for the game to be stopped earlier than it was, as early as literally from the time the incident took place."
Cowboys coach Paul Green labelled the incident a "debacle" and "disgrace", and claiming the referees failed in their duty of care.
Scans later revealed Macdonald suffered a fracture and dislocation of his left ankle that could rule him out for up to six months.
Annesley denied there rules regarding treatment of players on-field were changed over the summer, with referees given discretion on when to stop the game.
Currently, play can be halted if a club trainer tells a touch judge or official that one of their players is down with a serious injury.
Annesley said there was proof that was the case on Saturday.
"There is evidence on the tape that the trainers did try to get the attention of the referees," he said.
"They've got a lot happening so it's not that unusual for referees to have their attention drawn to other matters when play is still continuing.
"But there were enough officials on the field and in the grandstand to observe that there was a serious injury.
"We don't believe the rules require any adjustment.
"What took place on Saturday night wasn't to the standard that we expect and as a result, and other incidents in the game, the match officials will be relegated."
Australian Associated Press