The Frenchman was involved in an incident in the Eagles’ final away game of the season at Everton.
The Merseyside-based club came from 2-0 down to win 3-2 thanks to three second-half goals. The comeback sparked a pitch invasion at Goodison Park following the full time which saw Everton fans goad the Palace players and manager.
Footage emerged after the game, which appeared to show Vieira kicking out at an Everton fan who proved him as he made his way to the away team dressing room.
“The Everton incident is bigger than [just] that incident,” explained Vieira.
“There was a lot of pitch invasions that caused trouble. There are real issues here to reflect on and see the best ways to manage it.
“You don’t know what can happen. When you don’t know what can happen, you fear for anything for the players.
“We want to be safe, and the best way is to find the best way for those kinds of things not to happen. We want to be safe in our workplace. There is a big issue for the FA and Premier League to deal with.
“They need the support and the club and players to get involved as well. It’s not only the FA, everybody has to take responsibility and see the best way for those things not to happen.”
The 45-year-old Palace manager is being investigated by the Football Association because of the incident.
When asked whether he would accept any form of punishment should the FA come to that conclusion, Vieira responded: “I’m not there yet.
“I will participate with the FA and talk about the incident and give my opinion and view, but it’s not about that incident, it’s happened too often in the last couple of weeks.
“We need to reflect and make a decision so players, staff and fans can be safe.”
PICTURE: KEITH GILLARD