The initiative, in the form of a one-point lead, in the race for the top four was handed back to the Gunners after the Toffees' home defeat to Crystal Palace last week.
Arsene Wenger's side have the easier-looking run-in with games against Newcastle, West Brom and Norwich - compared to Everton's Southampton-Manchester City-Hull combination - but Martinez believes they will slip up
"I think it is fair to say, just looking at the last 15 years or so, fourth place is well below 76 points," said the Spaniard, whose side currently have 69 points.
"There has only been one season where you have needed 76 points for that (fourth) and on average it's always been a lot less points.
"You don't go far wrong when you look at the points tally. We are well aware anything around 72 to 75 points is Champions League football so we are desperate to try to make sure we get that.
"It doesn't matter who you are playing against or who you are fighting against to get into that fourth spot it's always the points tally that matters.
"I will go as far to say if you get nine points and you don't get into the Champions League, you can be proud and very happy any way.
"That's the target we are giving ourselves - how many points we can get from now until the end of the season.
"We have to make sure that we are fresh, we have recovered and look at every game as a unique opportunity to show what we can do."
Everton's small squad, already without midfielders Darron Gibson and Steven Pienaar, defender Phil Jagielka and strikers Lacina Traore and Arouna Kone, will be depleted further by the absences of forward Kevin Mirallas and centre-back Sylvain Distin.
Mirallas has already been ruled out for the remainder of the campaign with a groin problem sustained in Sunday's win over Manchester United while Distin is waiting to hear in the next 48 hours whether a hamstring injury has prematurely ended his campaign.
Martinez, however, rejected suggestions the size of the squad had contributed to the recent spate of problems.
"Sylvain has played a lot of games this season and has never had a sign of showing fatigue so I would say that was just an action in the game which resulted in an injury," added the Toffees boss.
"With Kevin Mirallas it is the last action of the game and it is an accident as he is trying to reach for the ball.
"I was well aware of making sure the last seven to eight weeks of the season was not a strain for a specific players, particularly the forwards, and we shared the playing time really well.
"I don't think any of the injuries are down to fatigue or lack of planning.
"In football you are going to get contact and sometimes you will be unfortunate but they are not injuries which are down to the minutes players have played."
Traore has featured for just 61 minutes in a single appearance since arriving on loan from Monaco in January and is unlikely to feature again.
But Martinez has not ruled out the prospect of retaining the services of the Ivory Coast international next season.
"We will sit down in the summer and review the situation," he said.
"I know Lacina is frustrated he has not been able to play more minutes for us.
"We need to speak to his parent club and see what their thoughts are but he is a very interesting player for us."
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