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.
"But we could lose to Arsenal, win all our remaining games and still make the Champions League depending on results.
"We still have to go there and think this one might have that rider on it but if we didn't we will still be trying to get a Europa League spot.
"Unfortunately it looks like it can only go to fifth this year so if we can't finish in the top four we will try to finish fifth instead.
"But it makes a change people asking me about finishing in the top four and maybe finishing in Europe.
"If you are a bookmaker you wouldn't be making Everton favourites to make the Champions League, they would be the underdogs and the big outsiders.
"I think it (the underdog tag) can help at times but you'd rather be favourites because people are realistically giving you the true position of where you are."
Everton have taken 13 points from their last five matches but history suggests a trip to the Emirates could burst their bubble.
Ever since the Gunners moved into their new north London home in 2006 they have been unbeaten against the Toffees.
Moyes' side have left with just two points from six visits but the manager insists there is a simple explanation for that record.
"Arsenal are a really good team with really good players, that is the reason for it," he added.
"They are a good side and always have been so we'll go there and try to pick a point up.
"We will go to Arsenal and try to win and get ourselves right in the mix.
"We have tended to do that this season but we've got a tough run-in and we could fade away and not having anything but at the moment we are in good shape."
Midfielder Darron Gibson, goalscorer on Saturday, is likely to require surgery on a thigh problem at the end of the campaign.
The 25-year-old missed nearly three months from September with the injury and he sat out almost all January and although he has returned to the starting line-up on a regular basis he is still hampered somewhat.
"He has got a bit of a problem at the top of his thigh which will probably require an operation at the end of the season," said Moyes.