The unidentified Raiders fan hit Webb in the back twice with his hand and a third time with a helmet before the second-year cornerback reacted. Webb swiped at the fan with his right hand as the brawl broke up.
"Two teams going after it and happened to be some fans, too," Webb said. "Hey man, it happened. I wasn't expecting that. But whoever jumped on my back, I had to get them off. Hey, you got to let them know, man, the only thing protecting you is this fence."
The Cowboys tweeted a photo of the two teams skirmishing Tuesday evening:
The brawl started when Cowboys cornerback Morris Claiborne slammed Raiders tight end Mychal Rivera to the turf by the sideline, just a few yards from a section of the crowd that was predominantly Raiders fans. There was an agreement that there would be no tackling at the practice, but Claiborne said he decided to take down Rivera after the tight end lowered his shoulder.
After Claiborne walked over Rivera and celebrated his tackle, Oakland receiver Greg Little rushed over to confront the cornerback. Within seconds, dozens of Dallas defenders and Oakland offensive players were brawling within reach of fans behind a fence.
When asked if Webb could face punishment from the league for shoving the fan even if he was provoked, NFL vice president Greg Aiello said, "No plans to do so."
"Training camps are team-operated and fall into the category of 'team matters,' " Aiello said.
Dallas coach Jason Garrett, who called the atmosphere of having Cowboys fans on one side of the facility and Raiders fans on the other as "electric" as he's ever seen at a practice, praised the way the players handled the brawls. He said the Cowboys have no intention to discipline Webb for his actions.
"You have to as a player defend your teammate, get yourself in there and make sure he's OK," Garrett said. "Always have your guy's back. That's an important part of building a football team. At the same time, poise in that situation is important. I thought we demonstrated both and you kind of move on."
For Wednesday's practice, there was increased security on the Raiders fans' side of the field.
"That passion, that's mostly what I'd hoped what we would get out of getting these teams together," said Cowboys owner and general manager Jerry Jones, who half-jokingly praised the remarkable power of Raiders offensive lineman Austin Howard's uppercut punches.
Another brawl broke out between the Cowboys' offense and Raiders' defense on the final play of the practice."I just ran over making sure all my brothers are good," Webb said. "I've got all my brothers' back. Everybody knows that. I mean, we just got into it, man."
ESPN.com Cowboys reporter Todd Archer contributed to this report.