Vieira was surrounded by jubilant Everton fans following the final whistle at Goodison Park on Thursday after the home side came back from 2-0 down to seal a 3-2 victory with a last-gasp winner that secured the Merseyside club’s Premier League status.
As the former France international was walking off the pitch to the away dressing room, he appeared to be repeatedly taunted by a fan and then reacted by attempting to kick out at the supporter.
Both the Football Association and Merseyside Police are looking into the incident — one of several recent worrying examples involving fans, players and coaching staff.
Vieira, speaking publicly for the first time about what had happened to him in midweek following Palace’s season-ending win at home to Manchester United on Sunday, said: “When you look at it in the Premier League, there were a lot of field invasions that can cause trouble.
“You don’t know what can happen. When you don’t know what can happen of course you fear for anything, for the players.”
The former Arsenal and France star added: “As a coach, manager, player or staff we want to be safe in our workplace.
“I think there is a big issue on the FA and Premier League’s plate to deal with.”
There was another troubling pitch invasion on Sunday, with Aston Villa manager Steven Gerrard saying goalkeeper Robin Olsen had been attacked when Manchester City fans poured onto the pitch to celebrate their side’s dramatic Premier League title triumph.
In a repeat of the ugly scenes at Goodison, supporters rushed onto the pitch both after Ilkay Gundogan’s winning goal and in greater numbers at full-time.
A Nottingham Forest fan was jailed this week for headbutting Sheffield United captain Billy Sharp after Tuesday’s Championship play-off semi-final, second leg.
There were also scenes of disorder at Port Vale on Thursday, with Swindon manager Ben Garner saying his players were “physically and verbally abused” following their League Two play-off semi-final defeat.