The Madrid side have the lowest budget in La Liga and were one of the favourites for relegation, but they are currently 10th in the league table and still in with a shout of finishing in the top seven, which would earn them European football next season.
"We all want to achieve European qualification," the Montenegro international told the club's website.
"It would ease the club's financial problems, which is vital, but it would also give us recognition.
"It's been a long time since Rayo played in Europe and we have to try and give the fans that joy again. We want Rayo to be known outside of Spain once again."
Delibasic thinks Rayo must win three of their final four games to keep their European dream alive, and hopes to get off to the right start against Valencia, who they host tomorrow.
"We'll have to pressure Valencia for the 90 minutes, be bold, go forward and try and create more chances than them. It's been a while since we won at home and now is the time to do it again," he said.
Valencia coach Ernesto Valverde believes his team cannot afford any more slip ups in their final four games of the season, as they seek to keep pressure on Real Sociedad in the hunt for the final Champions League spot.
Last weekend Los Che cut their gap on the Basques in the race for fourth down to two points after they thrashed Osasuna 4-0 and Getafe unexpectedly beat Philippe Montanier's side 2-1, ending La Real's 15-game unbeaten run.
Valverde insisted he had not lost faith in his team's chances even after they suffered a demoralising 4-2 defeat at Real Sociedad two weeks ago, but stressed that only a win would do against Rayo.
"If we want to get into the Champions League we cannot mess up again, we have no margin for error," he told reporters.
Valverde was doubtful about Tino Costa's hopes of recovering from an ankle sprain in time for the game, and confirmed that Sergio Canales would not travel to Vallecas due to a hamstring injury.
Rayo full-back Tito has been ruled out with a hamstring injury which could force him to miss the rest of the season, while winger Lass Bangoura is a doubt due to an ankle sprain he suffered against Osasuna a fortnight ago.