The Aragon club occupy the final position above the relegation zone and have not won any their last seven games in the Primera Division.
They host fifth-placed Valencia on Saturday evening and Sapunaru is insistent that only a victory will do.
"We have to win, because we need the three points," he said in a press conference today.
"I don't care if we are facing Valencia or anyone else, we need the points."
The Romanian also believes his side's recent results have not been a fair reflection of their performances on the pitch.
"We haven't deserved to lose so many games," he said.
"We have to work even harder than we have up to now to get out of the bottom part of the table.
"We haven't had any luck, but we have to keep working and give our all in every game."
Manolo Jimenez's side will be without goalkeeper Roberto Jimenez, who had to be taken to hospital today after being struck in the kidneys during a training session.
Jimenez has played every league game this season and his place in goal against Valencia will be occupied by Leo Franco, who has been the club's goalkeeper in Copa del Rey ties this campaign.
Valencia go into the game aiming to get their fifth consecutive away win in the league, and victory in La Romareda would see coach Ernesto Valverde equal former boss Unai Emery's record for successive wins on the road.
"I am not too worried by statistics now, but we are on a good run away from home and putting together four wins is not easy at all," said Valverde in a press conference.
"But we are not motivated by statistics, we are motivated by gaining fourth place," added the coach, who warned that Zaragoza would not be easy opponents.
"We'll have to adapt to the game, Zaragoza will put a lot of pressure on us. They have slipped towards the bottom of the table and they are used to playing a tough game and making things difficult for their opponents."