After practice, coach Ron Rivera said the scuffle began because Norman gave Newton a stiff-arm at the end of the play.
"The thing that we preach to the defense is that they score," Rivera said. "And so, even though I blew the whistle, Josh kept going like he's taught and the offense continued to react.
"What happened was Cam got stiff-armed in the helmet, and that's where that escalated. The big thing we have to understand is: 'Hey, you're going to get stiff-armed. You've just got to handle it."'
Newton had to be pulled off by teammates and called Norman a "pissant."
In the dustup, Newton also said, "Hit me like that again and you'll know something."
Newton and Norman continued to yell at each other later in practice. Newton shouted: "I bet you won't do that again."
Rivera didn't mind that Newton chased Norman at the end of the play.
"He's a football player at the end of the day," Rivera said. "If he throws an interception, it might mean his tackling the guy before he gets to the end zone to give our defense a chance to stop them, he's got to do it."
"He talked about it; he understands his responsibility. And he understands what we're trying to do as a football team. ... At the end of the day we're all family."Ron Rivera on Cam Newton
Neither Newton nor Norman were allowed to speak to reporters as they left the practice field.
Rivera said the scuffle shouldn't be seen as a knock at Newton's leadership abilities. He said Newton talked to the team afterward.
"He talked about it; he understands his responsibility," Rivera said. "And he understands what we're trying to do as a football team. ... At the end of the day, we're all family.
"And the poignant moment, as far as I was concerned, was when I brought the team up he broke it down with the word family, which is what Cam was trying to express."
Rivera responded in the affirmative when he was asked if he has been with a team where a quarterback got into a fight, pointing to his time as a player with the Bears.
"Remember, I played with Jim McMahon," he said.
Tension has been building between Newton and Norman, who have exchanged verbal barbs the past few days.
Rivera wasn't concerned that Newton and Norman have been "chirping" at each other for the past week.
"The big thing about it is you've got to handle it, because it will happen in a game," Rivera said. "You've got to learn when you get to this situation, you deal with it, you handle it, you cope with it and come back better than the next time.
"Unfortunately, it got a little more physical than it needed to be."
The coach said fights are to be expected around this time of training camp but he wasn't pleased that his $100 million quarterback was on the ground risking injury.
"You really don't expect it to be your quarterback," he said. "... You look for the positive side of it. He stood up for himself. I know it's the quarterback, but you treat everybody the same."
Rivera had a longer-than-usual post-practice talk with players, who huddled in the middle of one of the practice fields on one knee.
Afterward, he and general manager Dave Gettleman spent a few minutes talking to Norman.
Rivera said he hopes that players ultimately took from the incident that Newton is "like any of us."
"He's willing to fight," Rivera said. "There's a lot of ways you can spin it. That was my message to the guys. I said: 'Hey, you know how I feel about fighting. I'm not a big fan of it. I know at the end of the day, guys, hey, we've got to come back and be the team that we are."
Rivera said he isn't worried about the incident spilling over into the dorms where players stay.
"No, absolutely not," he said. "That's one of the things they talked about. They brought it up, 'Hey, we've got to let it go.'"