A heated Johnson went toward Brown moments after the young linebacker angrily dragged starting center Jon Feliciano out of a melee. Instead of things calming down, Feliciano reacted by throwing a haymaker in Brown's direction.
Brown followed with punches of his own. Both players had their helmets on at the time, but fortunately neither was injured.
"The incident [Monday], I take full responsibility," Johnson said Tuesday during a news conference that was planned before the incident. "I'm remorseful. It can't happen. It won't happen again.
"I've apologized to the appropriate people. In particular, Cam. I have to be better than that. It's not what we're looking for. It's a regrettable incident that can't and won't happen again."
Coach Brian Daboll called the entire team together Monday after the fights and told his team that type of behavior was unacceptable. It is what losing teams do.
Daboll later talked with all the parties involved. It is not believed any disciplinary actions were taken. "He addressed it and he made it crystal clear," Johnson said. "So it's been addressed and we're moving on from it."
The Giants held a light practice in the intense heat Tuesday without incident. They play their preseason opener Thursday night against the New England Patriots.
The melee Monday started not long after running back Saquon Barkley lowered his shoulder and sent cornerback Aaron Robinson flying during a "thud" period. It seemed to anger the defense. Linebacker Tae Crowder had a little extra aggression the next two plays.
Feliciano took offense to Crowder's actions. The two went after each other three plays after Barkley's hard run, sparking the brawl.
"I would say really for everyone that was involved in that, that is not what we're looking to do. It has been addressed," Daboll said. "I spoke to the team. I spoke to the coaches. They know the expectations. We're not going to lose our composure like that."
Afterward, Giants players downplayed the incident. Daboll said he saw some of those involved in the locker room playing pingpong and eating together.
He didn't necessarily have a problem with Barkley's physical run. He did take exception to his team's overall reaction.
"There is learning experiences from everything that happens on a football field," Daboll said. "That was certainly one of them for everybody. I brought them in, I let them know what the expectations were, what the standards are.
"I like the competition. I like the physicalness. But you have to do things the right way, whether that is on the practice field or whether that is in the meeting room or whether that is on game day. I think it all kind of relates to one another. So we pride ourselves on doing it the right way."