Lazio president Claudio Lotito says he would "never have permitted" his club captain Stefano Mauri to meet with Ultras in the way Napoli captain Marek Hamsik did ahead of the Coppa Italia final last weekend.
Following fan violence before the match in Rome, it took a meeting between Hamsik and the ringleader of one of Napoli's hardcore fan groups for the cup final eventually to get underway with a delay of 45 minutes.
"I would never have permitted my captain to talk to the leaders of the Ultras," Lotito said at a Lega Serie A meeting in Milan, according to La Repubblica. "I'm not going to express any judgment on the behaviour of my colleagues, but I would have said no. We need to distinguish between fans -- those who are passionate about the game and support their side, respecting the rules -- and delinquents."
Lotito believes action must be taken to rid football grounds of those "delinquents," and said simply handing out stadium bans is not going to work.
"People who have already been condemned to eight to 10 years in prison are just going to laugh at that," he said. "We need zero tolerance, more severe penalties, cells inside the grounds and changes to the punishment of clubs, who end up having to pay despite doing all they can to prevent this.
"We also don't have enough stadiums owned by clubs. If a fan sees their stadium as their own home then they are going to show more respect for it."
Meanwhile, Napoli have been punished for Saturday night's events at the Stadio Olimpico, with the authorities announcing a stadium ban for their next two Coppa Italia matches.
The punishment was imposed because of the delay to the kickoff as well as the fans whistling during the national anthem and then invading the pitch at the final whistle.
Defeated finalists Fiorentina, meanwhile, have been given a one-game suspended sentence for their Curva Fiesole after their supporters made "territorially discriminatory" chants towards Napoli fans during the final.