Mario Beretta's side lie at the foot of the standings, 14 points adrift of safety with 11 games remaining.
Cesena's last victory came as far back as January 15 and they have collected two points since.
Beretta knows that only a miracle will see his side avoid the drop but has urged his players to stand up and be counted, starting on Sunday at Cagliari.
"We are in a difficult position," Beretta said. "But until there is hope, we have a duty to try.
"Whatever happens, we need to give everything we have.
"There are still 33 points up for grabs and we cannot give up.
"We owe it to our fans and to our club."
Lack of goalscoring has been Cesena's main problem this season with the team having found the back of the net just 16 times in 27 games.
The good news for Beretta is that striker Adrian Mutu has recovered from a muscular injury and will lead Cesena's attack this weekend.
Rivals Cagliari cannot afford to give away points as they lie one place and six points clear of the relegation zone heading into the encounter at the Sant'Elia stadium.
The Sardinians sacked Davide Ballardini following last week's 6-3 loss at Napoli - their third straight defeat - and reinstated Massimo Ficcadenti as his replacement.
Cagliari were 12th in the standings when Ficcadenti was fired in November and have since dropped to 17th.
"Sunday's game is pivotal for us," Cagliari striker Mauricio Pinilla said. "We need to win in order to get our season back on track."
Pinilla, who has recovered from a muscular problem that kept him out of action for two weeks, will play from the start.
The hosts will be without pivotal midfielder Daniele Dessena, who suffered a fractured collarbone in training this week.