Martinez was speaking after his side's 0-0 draw with Crystal Palace in the Premier League after United had progressed with a 2-1 win over West Ham United in their quarter-final replay.
The Everton boss is quoted by the club's official website, saying: "It is a really good opportunity to show what we can do because when we played them a few weeks back, we weren’t anywhere near the level that we should be. We want to get rid of that feeling.
"And secondly, we’ll enjoy it. We’ll be ready and all of our fans will have a fantastic time."
The last time that Everton faced Manchester United in an FA Cup semi-final was in 2009, when David Moyes's side made it to the final with a penalty shoot-out win following a 0-0 draw with a much-changed United side after extra time.
It is a massive game both in terms of both side's seasons and the future of the respective managers. Everton have struggled this season in the Premier League and are currently languishing in 12th place - with many of the opinion that they've underachieved with arguably their best squad in the Premier League era.
Louis van Gaal has come under a lot of pressure this season as he goes in search of his first trophy in his two years at the club with speculation that he will be replaced in the summer.
It is a difficult semi-final to call with both managers needing a good result. The winners of this tie are likely to be the favourites for the final, with Crystal Palace and Watford contesting the other semi-final.
On the two occasions that Everton and Manchester United have faced each other in the league this season, United have come out on top on both occasions. They were comprehensive 3-0 winners at Goodison Park in October, while at the start of the month, United edged out the Toffees at Old Trafford.