Gary Neville is still without a win in two games since taking over as Valencia coach after his new club had a man sent off and needed an Eibar own goal to rescue a 1-1 draw at the modest Basque side in La Liga on Sunday.
Neville was a surprise appointment to replace Nuno Espirito Santo and his first game in charge was Wednesday's 2-0 reverse at home to Olympique Lyonnais that ended Valencia's hopes of advancing to the Champions League knockout round.
The former England defender presided over another disappointing performance from the ambitious Singapore-owned club at Eibar, although they have been missing a number of key players, including captain Dani Parejo and midfielder Sofiane Feghouli, through injury and suspension.
Eibar had the better chances in the first half and took a deserved lead moments before the break when Sergi Enrich finished from close range after good work down the right from Ander Capa.
Valencia's hopes of getting back into the game were dealt a blow in the 63rd minute when defender Lucas Orban was dismissed for an innocuous-looking challenge on Dani Garcia in the penalty area.
Jaume Domenech saved Saul Berjon’s spot kick and Borja Baston blasted the rebound over the bar with the visitors’ goal at his mercy.
Valencia levelled five minutes from time when the ball ricocheted off home defender David Junca and squirted past keeper Asier Riesgo into the net.
Eibar defender Ivan Ramis was then shown a straight red card for felling Paco Alcacer when the Valencia forward was through on goal in the second minute of added time.
Valencia have 21 points in eighth after 15 matches, while Eibar, who have one of the smallest budgets in La Liga, also have 21 points in 10th, behind Valencia and ninth-placed Athletic Bilbao on goal difference.
Second-placed Atletico Madrid can draw level on 35 points with leaders Barcelona with a win at home to Bilbao later on Sunday before Real Madrid, two points behind Atletico in third, play at fifth-placed Villarreal.
Barca, the Spanish and European champions, let slip a two-goal lead and were held to a 2-2 draw at home to Deportivo La Coruna on Saturday before jetting off to the Club World Cup in Japan.
Malaga moved out of the relegation places when Croatia forward Duje Cop struck three minutes from time for the Qatar-owned club to snatch a 2-1 comeback victory at fellow strugglers Rayo Vallecano earlier on Sunday.