Palace - who sit rock-bottom of the Premier League table with just three points from 10 matches - face a stiff test against Roberto Martinez's side.
Everton have lost only once in the league and, despite sitting seventh, are just a point adrift of second-placed Chelsea.
Millen has asked his side to make things difficult for the Goodison Park outfit, knowing a win could spark a revival.
"We know it's a great challenge and there are some good players there (at Everton)," Millen said.
"We've had some close games at Selhurst. I don't want teams to come to us and enjoy their football.
"I said to the lads we're going to war on Saturday. I said if I'm going to war, who is going with me? I believe I have that.
"I don't feel, being around the place, that anyone has given up. We're not that far adrift from five or six teams.
"If we can get a couple of results in the next five games, we'll have a chance.
"We're lacking Premier League experience from top to bottom. But I believe with this group of players, we can stay up."
Millen again stated that he expected Palace to confirm Ian Holloway's replacement shortly, adding that he anticipates the Everton game will be his last in charge.
"Me being in charge, I've enjoyed every minute. But I think at this time, it's right for someone new to come in," he said.
"I do expect Saturday to be (my last game in charge). Who knows?"
Millen also spoke of the painful injury suffered by midfielder Adlene Guedioura, who will miss at least six weeks with a punctured lung and two broken ribs.
"It doesn't look good. The trouble with cracked ribs is that you can't exercise and you can't get your heart and lungs going," he said.
"Some injuries, you can keep your cardiovascular fitness up but with this injury you can't do anything."
