Martinez's side have won four matches on the bounce and are within six points of fourth-placed Arsenal with eight games of their campaign left to play.
That is one more than the Gunners, who they play at Goodison Park a week on Sunday in a contest which could go a long way to establishing which team is playing Champions League football next season.
They could close the gap to three points this weekend if they win at Fulham on Sunday and Arsenal fail to take anything from their home game against Manchester City on Saturday night.
Martinez, though, was not specific about his aims for European football next season, instead focusing on how well his team have played during his first year in charge.
"The only thing that matters is how many wins we can get between now and the end of the season but I do think it's been a real success in terms of the way we've played and the way we've performed for the majority of the campaign," he said.
"Now I'm looking at the next eight games and they're really important in terms of how successful a season it has been.
"It would be a real shame if we couldn't take the good work we've done this season into the next campaign and the best way to do that is to qualify for a European competition.
"It's not easy to get four straight wins in this league and I'm really happy with the application of the players. It excites me going into every game.
"To go to a team like Newcastle, score three goals and keep a clean sheet, gives you a really positive feeling to take into your next game."
Everton are 7/2 with Betfair to finish in the top four.