The Spaniard won the competition with Wigan Athletic last season, upsetting the odds with a last-gasp 1-0 triumph over Manchester City at Wembley in May.
And while the title may belong to his old club for now, Martinez reckons he still has one hand on the trophy - and he is not about to loosen his grip on it.
Speaking before Everton's trip to League One Stevenage on Saturday, the 40-year-old told The Liverpool Echo: "It would be hard to let it go.
"There is an affinity you develop with the trophy because it's so special.
"It represents all the strong values football should have; someone to have a dream and be allowed to chase it.
"We know we'll be tested on Saturday."
Everton have the prospect of a Merseyside derby on Tuesday but Martinez is confident his charges will not allow that to distract them from the task at hand.
"Every dressing room would react in a different way," he added.
"Our dressing room is quite simple in that respect. We still stick to the old adage of taking every game as it comes. We're very much looking forward to that.
"I'm sure that in other dressing rooms, and I've experienced it myself in my playing career, the players might find it very difficult to keep their attention on the game on Saturday when they have a big derby on Tuesday.
"But here, believe me, we are all focused and concentrating on the FA Cup game and want to be as good as we can in that. Then we'll move on."
