Martinez's side sit seventh in the Premier League after 27 games, nine points adrift of fourth-placed Manchester City.
Everton host struggling Cardiff City on Saturday, and will be favourites to boost their hopes of securing continental football next term by recording a fifth straight home win in the top flight.
|8/1||Everton are 8/1 with Bet365 to beat Cardiff City 3-0|
Martinez admits he is not specifically gunning for a place in the top four, but believes that a spot in Europe's premier club competition is still a possibility for the Merseyside club.
"We don't look at it that way [in terms of targeting the top four], 48 points at this stage of the season is a very, very good return and all we want is to try to get as many as we can," the Spaniard told reporters.
"Can you get top four? Mathematically you can. Looking at the points tally that you're going to need to get in those positions is still achievable.
"It would depend on how the other clubs react to the disappointment of not being involved in Europe, other clubs that are still in Europe. I think there are many aspects that are going to affect the final points tally in that top four."
While Champions League qualification may prove difficult, Everton are level on points with Manchester United in sixth, a position that will secure qualification to the Europa League.
And Martinez was quick to reject suggestions that qualifying for the competition would be a hindrance to Everton's domestic ambitions next term.
"I think it would be very easy for us to say we don't want to qualify for Europe and just let the season cruise through," the former Wigan Athletic boss added.
"Qualifying for Europe would be a massive, massive step forward because it would bring big football occasions that I feel we need to be able to develop into the type of team that we want to be.
"It's something that would allow us to grow as a football club. We're going to fight with everything to try and achieve that."