Mallorca currently sit second bottom of the overall standings, three points from safety with only two games remaining, and are preparing themselves to play Atletico Madrid on Sunday.
However, the lower part of the table is very congested and five teams - Celta Vigo, Real Zaragoza, Deportivo La Coruna, Osasuna and Granada - can still be relegated, along with Mallorca, come the final day of the season.
Luna, who is on loan at Mallorca from Sevilla, believes Monday's 1-0 win over Real Betis gave them the confidence needed to claim wins against Atletico and Real Valladolid and secure safety.
He told his club's official website: "I think the team needed it (the win against Betis), because it is true that in recent games, especially in Bilbao where the team made a great effort against a tough opponent with a man down, (we did not get anything).
"I think the win against Betis has given us quite a lot of strength.
"We cling to our own hope and desire and that of our people, the fans of RCD Mallorca - it is true that we have never done it (got nine points from three successive games), but hey, all spells can be broken."
Rock bottom Celta Vigo are four points adrift of safety and travel to Real Valladolid to play a must-win match.
Valladolid have moved clear of the battle for survival in 13th place but Celta have everything to play for as only a win would keep their hopes of staying in the Primera Division alive.
Fellow strugglers Zaragoza must bounce back from their demoralising 2-1 defeat at home to Athletic Bilbao, where Ibai Gomez's stoppage-time winner saw them miss out on a valuable point.
They face Betis in their penultimate game and Zaragoza right-back Jose Fernandez knows there is now little room for error.
"We have to recover," he told Marca.
"The match against Betis is key and you have to earn it and not think of anything else.
"I understand that the fans are angry because things are not working out."
Elsewhere, Osasuna will look to move closer to safety with a win over Sevilla while Barcelona travel to Espanyol and Real Sociedad look to keep their hopes of playing in next season's Champions League alive as they go in search of a win over Real Madrid.
Valencia, who are level on points with Sociedad but fifth on goal difference, will hope they fail to claim anything from Jose Mourinho's side while they aim to beat Granada, while in the other game, Getafe face Rayo Vallecano.