Valencia captain Enzo Perez said his side have hit "rock bottom" after another disappointing display at home which saw a section of fans boo club owner Peter Lim for the first time.
Los Che had 65 percent of possession against a Granada side that lie at the foot of the standings but drew 1-1.
The hosts fell behind in the first half but Portuguese winger Nani equalised two minutes after the restart for the draw at the Mestalla stadium.
"We are not playing like we do in training and like this, it becomes very difficult," Perez told Marca. "We have hit rock bottom in every sense.
"A point is of little comfort because in order to climb up in the standings, you need to win games. We need to be stronger when playing at home and we aren't achieving this.
"Playing the way we are doing, it's going to be hard to take points."
After the hosts fell behind in the first half, a section of supporters chanted: "Peter [Lim] leave now."
Lim's daughter, Kim Lim, has hit back at those fans by writing on her Instagram account: "Ask us to leave as much but the fact is we still own the club so ...yeah ha ha. Deal with it and move on."
Kim was also angry with those Valencia supporters who questioned her family's commitment to the club.
She wrote: "I think some of the Valencia CF fans can be quite crazy and stupid to think they can control or have any say over my actions.... if you can understand English I already said I am coming to Valencia to support during my Euro trip. So stop writing stupid comments.."
A photo posted by �� ��Kim Lim 林慧俐 (@kimlimhl) on
A photo posted by �� ��Kim Lim 林慧俐 (@kimlimhl) on
Valencia have won just one and lost four of their five home games this season and are 15th in the standings with 11 points from 12 games.
The arrival of coach Cesare Prandelli, who replaced Pako Ayestaran on Oct. 3, has failed to spark Valencia into life. Prandelli did start his tenure with a 2-1 win at Sporting Gijon but his team has mustered two points from four games since.
Valencia have failed to score more than two goals in any game this campaign but Perez says its the the club's defensive frailties that are costing them dearly.
Valencia have not kept a clean sheet since April 20.
"We give away childlike goals that you should never concede in La Liga," the Argentine midfielder said.
A poll by Valencia-based newspaper Superdeporte asked club fans on Monday what they thought the aim of the club should be and the majority voted that Prandelli's side should focus on avoiding the drop with a minority believing that the club could still compete for European places for next season.
"We need a cool head and to try to improve from our mistakes," Perez said. "If anyone has to pull the team out of this situation it is us, the players."
Valencia defender Ezequiel Garay said unity will be key.
He told Superdeporte: "We need to be more united than ever. We are in a difficult position but with hard work and sacrifice we will come out of it.
"We are not thinking about the relegation zone but we are looking up because with the players that we have, we can aspire to much more."
Valencia play away to Sevilla on Saturday.