With six Premier League games to go, the Toffees are three points behind fourth-placed Chelsea, having played one game more than the Blues, and the Scot admits that they are "underdogs" to reach the top four.
"This is a vital game and games are running out," Moyes told reporters. "If we have got any chance of making the Champions League, we have got to get something out of it. For the last month we have been thereabouts but we will be the underdogs.
"That said, the way we have been playing, it gives us a chance. We are still in there fighting for a European spot and that is a positive thing."
Arsenal is in third place, and the Everton boss is wary of the danger that the Gunners will pose on Tuesday.
"Arsenal are a really good team with good players. They are a good side - they always have been," Moyes said. "If you were a bookmaker, you wouldn't make us favorites to qualify for the Champions League. Can it help being underdogs? It can but I would rather us be among the favorites."