The Merseyside outfit are currently four points adrift of the Gunners, who currently occupy the final Champions League spot in the Premier League table.
If the Toffees win at Goodison Park on Sunday, Martinez's side will be one point behind Arsenal with a game in hand.
"We've earned the right to fight for fourth," Martinez said in Friday's press conference. "That's a good season so far. There are 21 points to fight for. It's down to how many we can get.
"When you're playing Arsenal, you need to be perfect, and there's nothing better to help that than playing at home."
Everton have seven games left to play in their campaign.