The Eagles take on the Merseyside outfit aiming to arrest a three-match losing streak in the Premier League which has followed an excellent unbeaten run lasting two months.
A key hallmark of Palace’s early-season form was their strength at home and, while Aston Villa won at Selhurst Park last time out, Vieira is keen to get back on track in front of their own supporters.
He said: “The fans will have a massive role and the home game has come at the right time I would say.
“When you need to win games, especially for us the next one, and you are at home, we know with our fans the support will be there.
“We will have to perform well and try to win, but we know the fans will have a massive part to play in our performance. Like always they will be there and that is why I am looking forward to the game.”
Defeats to Villa, Leeds and Manchester United have threatened to spoil the positive work achieved by Vieira and his staff since he replaced Roy Hodgson as boss in the summer.
The 45-year-old has delivered a simple message to his players this week in an attempt to help reverse their fortunes.
“I think consistency is the word that has been going around the team, because we don’t want to throw away all the good work and good play we had since the beginning of the season,” Vieira added.
“We are going through a difficult period, yes, but we were expecting that.
“The messages and the mood at the training ground is still the same but at the same time we know there are some details we have to improve to turn those games into a win.”
Christian Benteke and Jordan Ayew missed gilt-edged chances in the losses at Leeds and Manchester United while those games were goalless.
Another area of improvement for Palace is their use of the ball and they should enjoy a decent chunk of possession against an Everton side happy to sit back and counter-attack.
Rafael Benitez’s Toffees ended their own poor form on Monday with a 2-1 win over Arsenal, their first league victory since September.
But Vieira insisted: “I didn’t need to watch the Arsenal game to know how good and dangerous this Everton team can be. I think when you look at the players and manager, obviously this is a good team.
“Again, we are only talking about the games they lost or drew, but if you look at the performances I am sure there were some positives that the manager was happy about as well.
“For us it will be a challenging game, but I believe we have what it takes to win and that is our priority. We want to perform and focus on our performance which will allow us to win.”
Palace right-back Joel Ward will return from suspension to face Everton and fellow defender Joachim Andersen (hamstring) may feature after he returning to training this week. James McArthur and Nathan Ferguson are still absent.