Football “cannot afford to take the gamble” of a player or manager being seriously injured during a pitch invasion and authorities must tackle the problem “promptly”.
Professional Footballers’ Association (PFA) chief executive Maheta Molango said “very high-profile players” have expressed concerns about the recent spate of incidents.
There have been a number of pitch invasions after games in England in recent weeks with incidents of supporters attacking players.
A fan was jailed after headbutting Sheffield United captain Billy Sharp, while Aston Villa keeper Robin Olsen was assaulted at Manchester City.
Last week, Crystal Palace boss Patrick Vieira was also involved in an incident with an Everton supporter during a pitch invasion following his side’s Premier League defeat at Goodison Park.
And Swindon Town players were “physically and verbally abused” after their League Two play-off semi-final defeat at Port Vale.
“Who knows what can happen in the future. We just cannot afford to take a gamble on that,” Molango told The Sports Desk podcast.
“A lot of the time the feeling of impunity is what drives people to behave in a way which is not acceptable.
“Once people know that you’ll be traced, you’ll be tracked and you’ll be punished, then I think it would be an element that hopefully will help people behave better.”
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Molango said it was not for the PFA to come up with solutions, and stressed that the problems are being caused by a “minority” of fans.
But he said players have spoken about feeling unsafe in their workplace and said there is a sense that events where invasions have taken place have been “predictable”.
“I think we need to make sure that adequate lessons are learned based on what has happened and hopefully we can make sure people understand it,” he said.
“In the end, the pitch is the workplace of the players and the managers and I think sometimes we tend to forget that. I think every one of us would like to go to work thinking that he or she can be safe and I think that should be the goal.”
BBC Sport has learned that the PFA has provided an impact statement to the Crown Prosecution Service, which will be read out when cases of disorder at football go to court.
The statement, signed by PFA chair and Oxford United captain John Mousinho, says that players have been subjected to “targeted violence” and have been “left wholly unprotected and isolated during regular, mass pitch invasions”.
It said that they feel “a greater sense of vulnerability” because they are aware that any reaction, even in self-defence, might have “long-lasting consequences” because of their profile.
It continues: “Pitch invasions often occur at the end of an important game, when a player will already be in a heightened emotional state. Therefore, when a large number of fans run onto the pitch, often blocking off your exit and visibility of team-mates and staff, you quickly feel trapped and isolated.
“There is often an overriding sense that the situation is out of control.
“As a player stranded on the field, you quickly become outnumbered, surrounded and vulnerable.
“It is a frightening situation to experience. In what can be a chaotic environment – where you are being grabbed, bumped into and shouted at by fans – it is impossible to know who presents a threat and, potentially, who may be intent on causing serious harm.”
The statement also said that the family members of players can feel “helpless, scared and traumatised” when watching pitch invasions unfold.
The subject of pitch invasions is due to be high on the agenda at the EFL summer conference next month.
The FA said it was “reviewing our regulations to help stamp this behaviour out and to ensure the safety of everyone inside a stadium”.