Last season Martinez guided Wigan all the way in the FA Cup to victory in the final, but they were also relegated from the top flight.
His current side - fifth in the table at the moment, a point behind fourth-placed Liverpool - host Sky Bet Championship promotion-chasers QPR in the third round of the cup on Saturday.
And asked ahead of the game if winning the knock-out competition or securing a decent finish in the Premier League was more important to him, Martinez said: "I don't think you can choose - it's like asking who you prefer, mum or dad.
"It's such a difficult question because you want both in your life.
"While we are in the FA Cup we are going to give everything we have got.
"In the league so far we have been very, very good and we want to be even better in the second half of the season.
"We are full of energy and focused on making sure we finish the season as strong as we can."
Aston Villa boss Paul Lambert, whose team are 11th in the Premier League, has expressed his belief that the majority of top-flight managers would rather do without the distraction of the FA Cup, stressing "survival in the league is vital."
Martinez has some sympathy with that point of view, but he insists - despite Wigan's relegation last term - that a cup run is a good thing for a club overall.
Asked if he could understand Lambert's comments, Martinez said: "I can, because every manager knows what they have got and they are looking at their squads and they know the numbers they have.
"I'm looking internally, and we have a group of 21 or 22 players and I feel any one is ready to represent Everton, which excites me.
"If you are trying to push yourself through a cup competition and be as good as you can in the league I can understand every manager needs to assess that and make their decisions.
"But what I have seen over the years is that having a good run in the cup is always positive - positive because it brings competition for places and allows the squad to show different roles, and you can get the benefit out of that.
"Obviously it all goes down to the amount of players you have available."
He added: "Every club has their own situation and agenda, and you have to respect that, and nobody knows a football club better than their own manager.
"So when a manager says something, you should listen to it, because it means there is a real reason behind it.
"But from our point of view, we are excited - it is like a young boy with a fresh toy. We are looking forward to this competition and the squad is ready to compete."
With Martinez having indicated he will make changes for the clash with QPR, Everton striker Nikica Jelavic could make his first start since September, while it remains to be seen whether or not there will be involvement for defender Johnny Heitinga, who is seeking a move but turned down a transfer to West Ham this week.
There are no fresh fitness concerns in the Toffees squad but they will still be missing the players who were absent through injury from the 1-1 league draw at Stoke on New Year's Day, including defender Sylvain Distin (hamstring).
In QPR, they are facing an outfit regarded by Martinez as "probably the best possession team in the Championship."
The Spaniard will be going head to head with a managerial counterpart who has also overseen a surprise FA Cup triumph in recent years, with R's boss Harry Redknapp having led Portsmouth to the trophy in 2008.