"I am not going to sit here and allow poor decisions to go by just because of a rule and I am not going to allow referees not to talk in the way that they should to our players over years and I feel strongly enough about it," Robinson said.
"It was just soft on Anzac Day. We want to play a tough game and they were soft calls coming from the bunker, they were not good enough."
He also said Cummins had ongoing issues with the Roosters.
"Ben has been horrible and disrespectful to our players for many years and it has continued," Robinson said.
"We have had a good high percentage win rate until this year ... he speaks poorly to our players. He won't look them in the eye.
"The way that he spoke to (captain) Jake (Friend) during the game was unacceptable."
NRL CEO Todd Greenberg said both incidents were potential breaches of the NRL rules and the club would have seven days to respond to the breach notices before a final determination was made.
"We cannot stand by and allow any club to deliberately and blatantly attack our referees," Mr Greenberg said.
"Not only is it a breach of the rules which are there to protect our referees from abuse, but it sets a bad example to the rest of the game, particularly juniors.
"We know from experience that young people imitate their NRL heroes and attacking referees is simply not acceptable.
"We are also trying to encourage young people to become referees and public attacks like this do nothing to achieve that goal."
Mr Greenberg said the NRL recognised that referees, like players, make mistakes in games and it was not surprising that clubs were sometimes frustrated by calls which went against them.
"But there are proper channels to vent those concerns and they were not followed in this instance," he said.
"Our Referees boss, Tony Archer is happy to talk to any club about issues which arise out of a game and that is the right way to address any problems."
