Martinez's side enjoyed a remarkable run to the last 16 this year, only to fall to two extra-time goals in their second-leg clash with Rubin Kazan.
Although only 11th in the table, Levante still have a faint hope of a Europa League spot again ahead of Saturday's final game of the La Liga season with Real Betis at the Estadi Ciutat de Valencia.
Qualification for the competition is so convoluted the team winding up in ninth place could play in Europe next season.
For Levante, ninth is the best they can hope for, but they would have to beat Betis and hope Sevilla lose at home to Champions League-chasing Valencia and Getafe are beaten at lowly Granada.
It is a long shot, but Martinez said: "If there is a one per cent chance of being in Europe for a second year we will fight for it to the fullest and until the last moment.
"Last year we were totally dependent on ourselves, but now things have changed, although with the situation there is the hope of playing in Europe again."
Since the turn of the year, however, Levante have suffered a woeful run, winning just four of 20 league matches and losing 10.
Despite that, Martinez praised his players for their achievements this season, saying: "As we still have this possibility I have to thank them for their effort and allegiance.
"They have offered me the dream of consolidating myself in the elite and of playing in Europe. They have made me a better coach."
With Atletico Madrid finishing third in the league and winning the Copa del Rey, it means Betis, who currently occupy seventh place, are assured of Europa League football next term.
Coach Pepe Mel, however, has warned his players they are not on holiday yet.
"It's been difficult since finishing the match against Zaragoza (winning 4-0 last weekend)," said Mel.
"You have to convince the players there is nothing to celebrate, that we're not on vacation, that we still have one more game.
"Overall, it's been a good season with ups and downs, but the players have given everything and when they have done that you cannot ask for more.
"We are grateful to this group of players."