Vieira is facing an investigation after being filmed clashing with a taunting fan at the end of their defeat at Goodison Park.
Speaking about the incident for the first time, Vieira said: "I think the Everton incident is bigger than just that incident. When you look at it in the Premier League, there were a lot of field invasions that can cause trouble.
"There are real issues here to reflect on and try to see what is the best way to manage it and to deal with it. You don't know what can happen. When you don't know what can happen of course you fear for anything, for the players.
"We want to be safe and the best way to do that is we need to reflect on what is the best way for those kind of things not to happen on the field. 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. They need the support and the club and the players to get involved. Everybody has to take responsibility and see what is the best way for those things not to happen."
The FA are investigating the incident involving Vieira but also Everton and the behaviour of their fans.
Vieira added: "I am not there yet. I will participate with the FA and talk about the incident and give my opinion and my view.
"Again, it is not about just that incident. It is about all the incidents and it happened too often in the last couple of weeks and we need to reflect on that and make a decision so players, staff and fans can be safe going to watch football matches."
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