The incident happened just in front of Raiders supporters, one of whom jumped down and got himself involved. The fan allegedly struck Webb three times - once with a helmet - provoking a response.
Once things cooled down, Webb told reporters: "It was just two teams going at it and it happened to be some fans, too.
"Hey man, it happened. I wasn't expecting that. But whoever jumped on my back, I had to get them off. You've got to let them know that the only thing protecting you is the fence between us."
NFL vice president Greg Aiello has since commented that Webb will not be charged for the incident, as practice sessions are strictly 'team affairs'.
Cowboys coach Jason Garrett praised the two sides despite the brawl, and stated that the electric atmosphere added to the competitive nature of the session.