A trip to Wembley for what would be the Latics' first-ever appearance in the semi-finals of the competition awaits if they can get past the Toffees.
Martinez admits that prospect lends an "extra-special" dimension to this weekend's contest.
But asked this morning what it would mean to get Wigan - whose best run in the FA Cup before this season saw them eliminated in the 1987 quarter-finals - to Wembley, the Spaniard said: "I don't really think that far (ahead), because I'm very pleased to get to where we have got so far, but we have done nothing yet.
"It would be an incredible achievement (to reach the semi-finals), and that is why we are going to fight tooth and nail to get there.
"But until you get there, it is pointless to make an overall assessment."
Asked if he had allowed himself to dream about bringing a trophy to the club, Martinez said: "No - I think we are still too far (away).
"Ninety minutes is an eternity in football, never mind looking to the final.
"We are happy to look back at this year's competition and how well we have done. Now, going to Goodison Park in the quarter-finals is a real challenge, and that is the way we are looking at it.
"Then, if you can overcome that, it will be the moment to look at what is ahead and what that would mean.
"When you are facing a game that could make history, though, for any club that is always extra-special."
Martinez - whose side are currently 17th in the Barclays Premier League, separated from the relegation zone by goal difference alone with 10 games to go - has emphasised that retaining their place in the division is Wigan's priority.
He does feel, though, that continued progress in the cup may well prove beneficial for the Latics' league form, and has made it clear that he views Saturday's clash with Everton as an important opportunity for his team to bounce back from their 4-0 top-flight home defeat against Liverpool last weekend.
"I think with the stage that we are at in the season now, it is quite straightforward - we are going to try to win every game that is left," Martinez said.
"It is quite simple - we just take it game by game, and we understand the importance of being in the quarter-finals of the FA Cup."
Martinez has indicated he may once again give an opportunity to some fringe players - such as striker Callum McManaman and midfielder Fraser Fyvie - who have come into the team for Wigan's other cup games this season, while fit-again pair Adrian Lopez and Ryo Miyaichi are back available for first-team selection.
Defender Lopez and winger Miyaichi both featured in the Latics' Under-21s fixture against Nottingham Forest earlier this week as they continued their rehabilitation from hamstring and ankle problems respectively.
Martinez, whose squad has been hit by a host of injuries this season, said: "Adrian Lopez played 90 minutes for the Under-21s and Ryo played 45 minutes, so I do consider them fully fit and I think they are available now.
"Emmerson Boyce and Antolin Alcaraz have come through our two previous games, against Reading and Liverpool, well enough.
"So I do expect everyone to be available for selection apart from Ben Watson, Albert Crusat and Ivan Ramis. Probably this is the strongest we have been this season."
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