Everton had to play with 10 men after James McCarthy was shown a second yellow card seven minutes into the second period, but amid intense pressure they remained resilient and earned what was ultimately an impressive point and clean sheet.
United's 2-1 win in their quarter-final replay at West Ham earlier in the evening ensured they would face Everton at Wembley on April 23, but despite his team's disappointing 1-0 league defeat at Old Trafford earlier this month and the defensive lapses that have ruined their pursuit of a top-six finish, Martinez was adamant their performance against Palace proved that this time they will be "ready" for United.
"That resilience we had to show," said the Spaniard
"But that's not enough on its own, you need tactical awareness as well, and we showed that. We were very clear in what we wanted to do, and then it's about managing the game to allow us our threat as well.
"I'm very pleased to keep a clean sheet and to manage the game in that way is perfect timing. It's great to see we're learning from our hard lessons. Probably, the timing of this performance is perfect
"It all matters in the final weeks of the campaign. We've lost too many points late on. It's now you want to hit your top level. You want to shine in the last few weeks of the season.
"To play a semi-final of the FA Cup against Manchester United at Wembley is as good as it gets. We'll enjoy it and will be ready.
"It's the same weekend 50 years ago that Colin Harvey became a hero by scoring the winning goal in the semi-final of the FA Cup (against United). Maybe that's a sign of something to come, but it will be terrific to be able to have one of our players writing new history."