Gary Neville says watching his Valencia side get demolished 7-0 by Barcelona at the Nou Camp was one of his "worst experiences" in football.
Wednesday's loss in the Copa del Rey semi-final first leg has increased the pressure on Neville, who is without a league win in eight matches.
"I am not going to sleep well tonight," said the former England player, who insisted he would not quit as manager.
"This is one of the worst experiences I've ever gone through in football."
'Neville go now'
Soon after the match, #Nevilleveteya, which translates to Neville go now, was trending in Valencia on Twitter.
The former Manchester United full-back was appointed in December, his first managerial job.
"I last doubted myself 18 years ago," said Neville, as he was repeatedly asked about his future in the post-match news conference. "After that, I developed coping mechanisms to deal with situations. I'm fine."
Neville's younger brother Phil is also on the Valencia coaching staff.
Spain radio station Cadena Cope has claimed that Valencia owner Peter Lim will decide in the next few hours whether or not to sack Neville.
Uruguay's Luis Suarez scored four goals and world player of the year Lionel Messi netted a hat-trick for Barcelona, leaving Neville with just four cup wins from his 14 games in charge.
Valencia travel to Real Betis in La Liga on Sunday, 12th in the table and just five points clear of the relegation zone.
"The people I feel most sorry for are the Valencia supporters," Neville added. "They don't deserve a performance like that.
"We were playing against three of the best players in the world and we gave them three-on-twos I don't know how many times.
"It was unacceptable and we have to recover very quickly. We need to win a league game. I wish the match against Betis could start in 10 minutes."
Valencia sporting director Jesus Garcia Pitarch described the defeat as one of the worst results in the club's history.
"When I have moments like this I don't enjoy them at all, it was painful," added Neville.
"I stood out there both halves feeling helpless, trying to change it in some way, knowing the tide of the game was against us.
"We were playing against a fantastic team, keep that in perspective, but the scoreline is unacceptable.
"I need to make sure everything in the players' minds now shifts to Betis. Be clear, we have to deliver on Sunday. "
|Gary Neville's career|
|1992: Makes Manchester United debut and spends 19 years at club, winning 20 major trophies including two Champions Leagues and eight Premier Leagues|
|1995: Makes England debut going on to earn 85 caps|
|2011: Starts as a Sky Sports pundit for the 2011-12 season|
|2012: Appointed assistant coach to Roy Hodgson with the England team|
|2014: Agrees to buy Salford City with fellow former United players including brother Phil, Ryan Giggs and Paul Scholes|
|2014: Agrees to sell 50% stake of Salford City to businessman Peter Lim, already majority owner of Valencia|
|2015: Appointed Valencia head coach with brother Phil as his assistant|