Manager Gary Neville apologised to Valencia fans after an "unacceptable" 1-0 derby defeat by Levante.
Giuseppe Rossi, who played alongside Neville at Manchester United, earned La Liga's bottom club victory as Valencia lost for the fourth time in five games.
"You can't defend a performance like that," said Neville, who has won three out of 15 league games since he was appointed in December.
"I take responsibility and apologise to the fans."
Valencia are 12th in La Liga, eight points above the relegation zone.
Neville, 41, was appointed in December, on a contract until the end of the season, but has struggled in his first managerial role.
"It is unacceptable to play like that in a derby. We deserve all the criticism," he said.
"They are bottom of the table, but they fought for every ball.
"It is absolutely unacceptable and I have said that to the players."