The English Football Association is investigating all incidents of fans invading the field and has condemned their "anti-social behaviour" as completely unacceptable.
The FA's statement comes after Everton fans invaded the pitch at Goodison Park following Dominic Calvert-Lewin's 85th-minute winner and at the final whistle of Thursday's 3-2 victory over Crystal Palace, which secured their spot in the Premier League next season.
Palace manager Patrick Vieira was also involved in an altercation with a fan when he was walking towards the away dressing room after the final whistle.
The fan appeared to provoke Vieira with hand gestures, after which Vieira kicked him to the ground and had to be led away by other supporters.
"We are very concerned about the rise in anti-social behaviour from fans as we reach the end of the season," the FA said on Friday.
"Football stadiums should always be a safe and enjoyable space for everyone, and these incidents are completely unacceptable and have no place in our game.
"It is illegal to enter the pitch area in any stadium and these actions are putting players, fans and people who run the game at great risk. This simply cannot continue and we can confirm that we are investigating all of the incidences."
The FA said clubs needed to prevent pitch invasions from occurring and urged them to take their own action against those that break the rules and the law.
"The FA will be seeking to do all that it can to work with clubs as well as addressing the issues from a disciplinary perspective," the statement added.
West Ham United manager David Moyes said such incidents have been an "issue", while Arsenal manager Mikel Arteta said pitch invaders pose a danger to players and staff.
"We have to stop it and we have to minimise the risk and exposure of players and staff in this situation because you cannot control it. When there are so many people involved it becomes dangerous," Arteta told reporters.
There have also been a number of incidents of pitch invasions in England's lower leagues.
Nottinghamshire Police said that a man had been arrested and interviewed on suspicion of assault as part of an investigation into video footage showing an incident during Tuesday's Championship playoff semi-final between Nottingham Forest and Sheffield United.
Police did not provide details of the incident but a video on social media showed United striker Oli McBurnie, wearing a surgical boot, appearing to stamp on a fan on the ground during a pitch invasion after Forest won on penalties at the City Ground.
A Forest fan who head-butted United captain Billy Sharp during the pitch invasion was jailed for 24 weeks and handed a 10-year football banning order on Thursday.
Swindon Town manager Ben Garner said his players were "physically and verbally abused" after their League Two playoff semi-final defeat by Port Vale.
Swindon were beaten 6-5 on penalties by Vale, whose fans invaded the pitch after the last penalty and television footage appeared to show some in an altercation with Swindon players.