The Toffees sit just three points behind Chelsea in fourth place in the Premier League after putting together a run of five matches unbeaten.
Moyes, who has never won away at Arsenal during his time in charge of Everton, concedes that his team still have to prove they are capable of winning big matches on the road.
He told The Mirror: "I've said to the players that we're going to have to win away from home, and for the Champions League it might have to be more than one.
"It's us trying to break new ground in a lot of ways. We've got an opportunity and we'll try to take it. The players know this is a chance and because of that there's not a great deal that needs to be said.
"And it is a small chance, about 15 per cent. There are only five or six teams that can say they've got a chance so we're happy to be in this position. If we win this one, we'll be in with an opportunity. If we lose, our chance will probably go."
Victory at the Emirates would see Everton climb to fifth place in the Premier League above Tottenham Hotspur on goal difference.