Martinez guided Wigan to FA Cup glory at Wembley last year and his new side open this season's campaign with a third-round tie at home to QPR on Saturday.
The Toffees are also flying high in fifth place in the Premier League but Martinez is refusing to prioritise either competition at this stage.
"I don't think you can choose - it's like asking who you prefer, mum or dad," said the Spaniard.
"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 has expressed his belief that the majority of Premier League managers would rather do without the distraction of the FA Cup, and Martinez has some sympathy for that view.
He said: "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."