FA Cup semi-finals.In the process, they reached 66 points, a tally which Martinez knows is usually more than enough to secure a seat at Europe's top table, but which will not be sufficient this season.
Asked how many they might need, the Spaniard said: "It's hard to tell, but I think it's quite clear that it's going to be the highest it's ever been in Premier League history.
"At this stage with 63 points, you are always guaranteed to finish top four
Now, clearly, one team is going to be out of that with that return.
"The way the competition is going, it's always harder now to win the title, there are always three or four football clubs, and I think it's the same for the fourth place and so on.
"I do think it's a bit of an unknown."
Everton head into the remaining five games two points better off than the Gunners, but only after needing a helping hand to secure their seventh successive league win.
The victory was ultimately secured by Wes Brown's 75th-minute own goal, the sixth the Black Cats have conceded in the league to date this season, although the luckless defender knew little about it.
There was little he could do to prevent the impressive Gerard Deulofeu's cross from creeping inside the post after hitting him.
Sunderland otherwise gave as good as they got for long periods, although Steven Naismith had earlier passed up glorious opportunities to give the visitors the lead either side of half-time.
Asked if his men could go the distance, Martinez said: "That's our objective
We are going into new ground, as you can imagine.
"It's the highest points tally in Premier League history at Everton and that's a significant statement, with the history that we have and the heritage we have at the club.
"We are going to just take every game with a real excitement
We have got very much a group of players that is focused and desperate to play, good competition for places, so we are just going to take it step-by-step.
"But to have 66 points by this stage of the season is a remarkable achievement and the players deserve a lot of credit."
For Sunderland, the stakes are very different and a fifth defeat on the trot did their dwindling survival hopes little good.
Head coach Gus Poyet said: "If you need to show somebody somewhere in the world where they don't watch Sunderland every week, you show him this game and tell him this is the story of the season and that's it.
"You don't need to show anything else because that's it
Something always happens and that something is always, or most of the time, against us.
"I don't have a word because it's not one feeling, really
It hurts, it hurts because it doesn't matter what we do, something happens
And it's not an excuse, I don't really believe in luck.
Meanwhile, Martinez blamed a misunderstanding for a minor disruption to the minute's silence in memory of the Hillsborough victims before the game.
He said: "There were a couple of shouts, but I think it was people entering the ground and I don't think they were aware we were celebrating the minute of silence.
"We all know that football fans everywhere in the world have incredible respect for what happened 25 years ago, and today the silence in the ground was full of respect.
"It was a clear incident of a group of people walking in and I don't think they were aware what they were disturbing at that time."
Source : PA
Source: PA