Unai Emery's side have failed to win their past four games and they also lost the Europa League quarter-final first leg to AZ Alkmaar raising doubts about their European credentials. They have also registered just one home win since Christmas and so have earned the ire of many fans.
The side from the east are currently in third place but they are precariously positioned there as Malaga are just one point behind them. Also, Levante are in fifth place and just three points behind Valencia and so there has been a dramatic turnaround in fortunes for the two Valencian clubs.
Just weeks ago, there had been talk that Valencia could finally join the big two clubs of Real Madrid and Barcelona and be considered as outside contenders for La Liga next season as they held a commanding lead over the other clubs.
Emery, who is said to have met president Manuel Llorente after the game, was also disappointed by the result and called on his side to convert their superiority to goals and grind out the results necessary in the remaining games.
"We were on top in terms of openings, chances and possession but we lacked a finishing touch to demonstrate the superiority that we had," Emery told reporters after the game.
"At the moment it is very important that we keep the errors to a minimum as the results do not correspond to how well we are playing.
"The draw was poor and we are not happy. The fans have protested at the end but during the game they have supported us.
"I'm not worried about the possibility of losing the Champions League place but I do see the need to make changes and look for solutions."
Valencia are 25 points behind Barcelona who are in second-place and will have to carry out a summer of reconstruction if they are to ensure that they stand a chance of achieving progress after nearly three seasons out of the top two.