The Toffees host their London counterparts at Goodison Park on Saturday knowing that victory would propel them to within a single point of the fourth-placed Gunners in the standings.
However, the North Londoners have never failed to finish outside the top four in Arsene Wenger's 18-year tenure, and Martinez admits that the Frenchman has the know-how necessary to extend that feat this season.
"Being in this position gives us an understanding of what a good season we've had," the Spaniard told reporters. "With the points we have, we have a realistic chance to fight for that aim.
"I'm not saying we're going to get that because we admire Arsenal as they get in the Champions League consistently.
"They have developed a real understanding of what to do in these games, so that makes Sunday a phenomenal challenge."
Martinez's men moved four points adrift of Arsenal with a 3-1 win over Fulham at Craven Cottage on Sunday.