The Toffees beat QPR on Saturday to move within striking distance of the Champions League places, and the Scottish boss believes the tie against the Gunners is a must-win match
Moyes' team are just three points adrift of the top four following the win over the Hoops, and face a crucial clash with the Gunners on Tuesday which Moyes believes will define their season.
He told reporters: "If we can go and win at Arsenal I think you can say we've got a chance of being involved in the Champions League, I think if we don't then you can say we've got a chance of making the Europa League.
"No matter what happens I think the players have given themselves a great chance, there's five or six games to go, we've been doing it for most of the season why would it change, I expect the players to keep picking up victories and trying to win every game if we can.
"They've got a real resilience and a toughness to them the players, and because of that we keep at it and the players know what is expected."
The Merseysiders secured the points through goals from Darron Gibson and Victor Anichebe, and although QPR provided a sporadic threat, their manager Harry Redknapp feels survival is looking an increasingly unlikely prospect.
He said: "I felt we came in 1-0 down feeling a little bit sorry for ourselves and then we started the second half sloppy and came under pressure.
"At 0-0 in the first half I thought we looked dangerous, Remy's had a shot on the break, I felt we could pass our way through and and get through them, once we went one down we seemed to lose a bit of belief.
"You've got to keep going, what else can you do? You can't give up, you've got to keep trying, you've got to keep believing but it's getting more and more difficult.
"I can't say were down, if it happens it happens. What can you do, you've got what you've got, the club will have to regroup and have a look at what they've got there if that happens."