The Everton manager has witnessed his side produce a string of impressive Premier League performances this season, although two wins in their last six league games has left the Merseyside club in sixth.
Manchester City's victory in the League Cup means Everton's current position would see them qualify for next season's UEFA Europa League.
A UEFA Champions League spot is looking increasingly unlikely, however, with Everton trailing City in fourth by nine points.
But Martinez refuses to give up the ghost and wants to finish as high as possible.
"We've never had it in our aims to finish sixth," he told the club's official website.
"We want to finish as high as we can and that's still the case.
"Obviously when the season finishes, you sit down, see where you are in the table and see where that leaves you. But I would never look at this season as one where we're trying to fight for sixth position.
"We are sixth now and over the season it's about as low as we've been. In terms of results, I don't think the table reflects the season we've had.
"We've had a game postponed and, among others, we've had two results recently that didn't match the performances.
"So we are aspiring to finish the season as strong as we can and with as many points as we can.
"I don't think our aim will be finishing sixth at this present time."
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