The Spaniard insists he will watch Saturday's clash between Arsenal and Manchester City only as an interested observer despite the significance a win for Manuel Pellegrini's side would hold for the Toffees.
If the fourth-placed Gunners lose then Everton could move to within three points if they beat bottom side Fulham on Sunday and, with a match in hand and Arsenal to visit Goodison Park next weekend, Champions League qualification becomes a reality.
Neighbours Liverpool could also do them a favour by beating Tottenham, the team immediately below them in sixth, on the same day but Martinez stressed he is not relying on anyone outside of his own club.
"You'll get dizzy if you start looking at what the others can do," said the Everton boss.
"It is easier than that. You look at the points you can get and if it is big enough you can look at trying to achieve top four and finishing the season with European qualification.
"There are many twists and turns, the league this season has shown anyone can beat anyone or drop points where they are not expected to.
"I will watch it (the Arsenal game) because I am always curious and I am a football fan in that respect but I will watch it with an open mind.
"It is not that I am not wishing one result or another, I am quite open-minded in that respect.
"It doesn't matter what the others will do in terms of having a successful season, it will be down to how many points we can get.
"I have learned in the past when you are trying to pre-plan it never works out that way.
"All that matters is we try to be as good as we can be and try to get as many points as we can.
"I guarantee if we reach a certain level we will achieve our aim, it doesn't matter what others do.
"It would be a dream to be involved in Europe next season."
Four successive league victories have put Everton within touching distance of the top four again after falling off the pace in February.
Martinez believes the momentum they have generated has given the squad the lift it needed heading into the final six weeks of the season.
"It is not easy to get four straight wins," he added.
"I am really happy with the application of the players and when you have the possibilities we have at the moment it excites me every game.
"Going to Newcastle (in midweek), scoring three goals and keeping a clean sheet gives you a really positive feeling and confidence heading into the next game and we don't want to lose that.
"When you look at the players, they are fresh, enjoying their football and they are working with real desire.
"We will push ourselves to get as many points as we can. The only thing that matters is how many wins we can get.
"I do feel this season has been a real success in the way we have played and performed.
"The next eight games are really important to end up with a good season.
"It would be a real shame if we could not take the good work we have done this season into the next campaign and the best way to do that is qualifying for a European competition."
Martinez already has an eye on the future as he is looking to revamp the club's Finch Farm training complex, which is already one of the best in the Premier League.
"In general it is important we try to get accommodation inside to use for the first team and youngsters," he said.
"It is about trying to increase the possibilities we have and having the players stay overnight in terms of preparation for home games and short-distance away games.
"There are a few exciting plans ahead of us but it is still on the drawing board and we will get a final sketch in the next four to five weeks."
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