The Toffees, after beating Swansea 3-1 earlier on Sunday, were denied another Merseyside derby clash by the Gunners' 2-1 win over Liverpool in the later match.
While a trip to the Emirates Stadium holds slightly less of an attraction, it is just as great a challenge for Martinez's men - who earned a credible 1-1 draw there already this season.
"You always hope to have a home tie but, if you want to win the cup, you need to be able to face anyone wherever it is," said the Spaniard, who is looking to become the first manager to win back-to-back FA Cups after leading Wigan to Wembley glory last May.
"If you want a word it is professionalism: we were professional against a Championship team QPR in the third round and then in the fourth round away at a League One side at Stevenage.
"(On Sunday) we were professional and a Merseyside derby would've been just perfect to show if we can win the cup or not.
"But it is the same for Arsenal away, so we will have to be at our best."
The match against a Swansea side, who made eight changes with a Europa League tie against Napoli to come this week, looked to be drifting at 1-1 in the second half after Jonathan de Guzman's header had cancelled out a goal on debut for the Toffees' on-loan Monaco striker Lacina Traore.
The introduction of Steven Naismith on the hour changed all that as within four minutes he had latched on to Neil Taylor's backpass to score his fourth in five matches, and he then drew the foul off Ashley Richards to allow Leighton Baines to score from the spot.
He then went off with concussion before the end, leaving Everton to finish with 10 men, after failing to recover from a clash with Jordi Amat.
"We will check him over the next 24 hours as he had a bit of delayed concussion with the knock," Martinez said.
"He was okay and then all of a sudden he became dizzy and he couldn't remember what was happening and we couldn't take any risks.
"He has played in different positions but when he is central he is at his best, he was instinctive, a real threat and he is enjoying his football."
Swansea caretaker boss Garry Monk denied he had picked a side with Thursday's game in mind.
"That wasn't my thought going into the game. I have only been thinking about the next game, it is the truth," he said.
"I put a team out that I thought could win the game and for an hour we weren't far away.
"When you have got seven games in 21 days it is impossible to play the same 11 in every game.
"It is a squad game. Everyone seems to be amazed when there are rotations."
The sixth-round draw threw up a repeat of last season's final, with Manchester City hosting Wigan, while there remains the prospect of a Sheffield derby in the last eight after League One United came from behind to beat Championship club Nottingham Forest 3-1, with Wednesday's clash against Charlton postponed on Saturday.
Chris Porter scored twice in stoppage time for the Blades after on-loan Liverpool midfielder Conor Coady had equalised Jamie Paterson's headed opener.