The Toffees sealed their passage to the last eight of the competition with a 3-1 win over Swansea City, and though Martinez was disappointed not to be playing at Goodison Park again, says he would relish a tie against Brendan Rodgers' side or Arsenal.
"Obviously in the draw you're hoping for home tie, but it doesn't matter because if you want to win the cup you need to be able to face anyone," he told reporters.
"I think a Merseyside derby would be perfect to show if we can win the FA Cup or not, but it is the same if we play Arsenal away. They are both in very good moments of form this season, so we will have to be at our best.
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Martinez, who won the FA Cup in 2013 with Wigan, admitted that he was pleased with the way his side battled to victory against the Welsh side, while he also praised debutant Lacina Traore, who marked his first appearance in England with an early goal.
"I am very satisfied, because all you are looking for is a win to get into the next round. It was a good game of football in the first half, and because of the fresh legs Swansea had they brought a good approach to the game.
"I thought we were a little bit anxious and feeling the role of being expected to get through to the next round. In the second half it was much different. We controlled the game and limited Swansea to very little.
"I was very pleased for Lacina Traore to play 60 minutes was a real success for us. To play against a team like Swansea is a nightmare for a player coming into our league, and I thought he coped with the instructions off the ball really well.
"He scored within two minutes of his Everton career, which is a beautiful sign for the future."
Meanwhile, Swansea player/coach Garry Monk was content with the way his much-changed side went toe-to- toe with the home side, and admitted he did not blame Neil Taylor for the error that led to Steven Naismith's match-turning goal.
"We took the game plan as we wanted and we were well in the game. There was an individual error from Neil but I can live with that," he said.
"We finished the first half positive and could have gone on to do something so we’re frustrated."