Defeats by Sweden and Russia have sealed the fate of the surprise Euro 2004 winners, who have yet to score a goal at the tournament and never looked like getting back into either game.
"Our aim is not to finish our matches here without points," defender Yannis Goumas told reporters as he prepared for Wednesday's game in Salzburg.
"Our disappointment will be even greater if we fail to win points against Spain and we will do all we can to avoid this from happening."
Summing up the mood, he added: "We must go out and honour our flag and our national strip so as to make this experience here less bitter."
Defender Christos Patsatzoglou said Greece are fully aware of the strength of the Spaniards, who have already qualified for the quarter-finals after winning both their group matches -- including a 4-1 drubbing of Russia.
"It will be a tough match for us. We know it will not be easy," Patsatzoglou said.
"But we will go out fighting, playing for us and our fans".