The visitors have won five Premier League games in a row to climb to within four points of fourth-placed Arsenal with a game in hand and they welcome Arsene Wenger's side to Goodison Park next Sunday.
Arsenal have faltered in recent weeks having picked up just five points from a possible 15, prompting Wenger to talk about the need to look behind them at in-form Everton.
"We admire Arsenal and we know they've been getting consistently in the Champions League for the last 18 or 19 years," Martinez told reporters. "That develops a real understanding of what to do in this sort of game.
"So for us the challenge against Arsenal on Sunday is phenomenal. It's a welcome one but if reflects again what a good season we've had.
"When you speak about the league you always work hard over eight or nine months to see where you're going to be in the final eight games of the season.
"It's fair to say with the amount of points we have we've got a realistic chance to fight for that aim.
"Arsenal looking over their shoulder at us is a great compliment but we're looking over our shoulder as well," he added.
David Stockdale's own goal was cancelled out by a fierce drive by Ashkan Dejagah before Mirallas and Naismith added late goals to seal the win and set up next weekend's game perfectly.
Everton have turned Goodison Park in to a fortress this season having won 11 and lost one of their 15 home games.
"We embrace the challenge," Martinez added. "We really enjoy playing at Goodison. We have created an incredible relationship between the fans and the players.
"We have a real advantage for playing at home. We feel if we are perfect in what we do we've got a great chance to get points and that's the way we're going to approach the final seven games."
Fulham were vastly improved from the side who were dismantled 5-0 by Manchester City last weekend and could count themselves unlucky not to take at least a point from the game.
However, their survival is now looking increasingly unlikely as they are five points adrift of the relative safety of 17th Place with six games left.
Manager Felix Magath said it was the team's best performance since he arrived at the club.
"I'm disappointed for today. We have to go out and try next week again. I know we can still make it," he said.
"It was a very important game today and unfortunately we lost. That's very disappointing. If you had seen the game how we play it was our best game until now. I'm ready to stay here and work in the Championship."
- Sports & Recreation
- Arsene Wenger
- Goodison Park
- Premier League
- Steven Naismith