Real Madrid director Emilio Butragueno refused to guarantee coach Rafael Benitez's future after his side's 2-2 draw at Valencia.
Paco Alcacer scored an 83rd-minute equaliser as Gary Neville's men twice came from behind to earn a point in La Liga on Sunday.
Madrid played the final 22 minutes with 10 men after Mateo Kovacic was sent off, but they were unable to hold on despite Gareth Bale's late goal.
Butragueno had given Benitez his backing late last year, but was less forthcoming when asked after the Valencia draw.
Asked if Benitez would be discussed at a board meeting on Tuesday, Butragueno told Movistar+: "I think the team offered a good image.
"The circumstances didn't help, but even with 10 men the team could have won at the end. There has to be calm."
Karim Benzema had put Madrid ahead before Dani Parejo equalised from the penalty spot on the stroke of half-time.
Butragueno felt Benitez's men had performed well as they were left in third in the table, four points behind leaders Atletico Madrid.
"I think the team put in a good game, I really do," he said.
"We know how difficult it always is for us to come here, and today, the circumstances didn't help - we were a player down, however we didn't lose control and we could have scored a third even with a man less.
"We didn't lose composure but we didn't achieve our objective which was to win here. The path we are on isn't bad."