The Toffees moved to within three points of fourth-placed Chelsea, who have a match in hand, and four of the Gunners in third after beating QPR 2-0 at the weekend.
For that reason the meeting at the Emirates Stadium, where Everton have a woeful record, has been billed as make or break for the Merseysiders' top-four hopes.
But while Moyes knows it is a significant match he refuses to accept they will be knocked out of contention if they lose.
"It is a vital game now because games are running out," he said.
"I think if we have any small chances of making the Champions League we have to get something out of it and peg back Arsenal, Chelsea and Tottenham.
"We are the big underdogs to get anywhere close to that but the way they have been playing keeps us hoping there is a real chance.
"There is a lot to lose because if we didn't win it the media would be the first to say we wouldn't make the Champions League.
"But from the other point of view we feel no matter what happens we are still in the fight for a European spot and for Everton to be saying that at this stage of the season is a positive thing.
"Maybe after Tuesday night you could be saying Everton won't make the top four but probably for the last three months people have been saying we won't make it."
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