Manchester United boss Louis van Gaal said he could "quit by myself" after Stoke City beat his side 2-0 to condemn them to a fourth straight defeat.
The Dutchman, under pressure after seven games without a victory, was asked at his post-match news conference whether he feared he would be sacked.
Van Gaal, 64, said that was something he would discuss with executive vice-chairman Ed Woodward and not the media.
"It is not always the club that has to fire or sack me," he said.
"Sometimes I do that by myself, but I am the one who wants to speak first with the board of Manchester United and my members of staff and my players, not with you."
United's miserable run has seen them knocked out of the Champions League at the group stage and slip out of the top four in the Premier League.
Van Gaal, who succeeded David Moyes in the summer of 2014, said the club had backed him "all the time" but added: "We have lost so there is a new situation.
"I feel the support of my players and my board. The fans will be disappointed but that is logical after four defeats."
Van Gaal does not think it is important that Woodward has not publicly supported him.
"For me it's much more important that people are saying that to me," he said. "I am not so interested in public sayings."
Juan Mata wipes his face after Manchester United's 2-0 defeat at Stoke
United have lost four straight competitive matches in a single season for the first time since November 1961
Van Gaal saw his side quickly go behind to goals from Bojan Krkic and Marko Arnautovic, and United struggled to create chances as they tried to work their way back into the match in the second half.
"We have lost the game in the first 45 minutes because we didn't dare to play our football," said Van Gaal, whose side host Chelsea on Monday.
"The circumstances now play a bigger role and will in the next game also. We have to cope with that and look for the solution.
"It is very difficult as I'm also part of four losses and I have to cope with that and I have to manage that. More important is that my players shall manage that because they have to perform."
Man Utd embarrassing - Shearer
Match of the Day pundit Alan Shearer described United's first-half performance as "pathetic".
Van Gaal had walked out of his pre-match news conference after less than five minutes, having asked reporters if any of them wanted to apologise to him for speculation about his future.
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Van Gaal walks out of news conference
Former England striker Shearer said: "Van Gaal decided to take on the media this week and he picked a team he thought would scrap for him and that was the best they could do for him - that was embarrassing.
"On today's evidence, the players are not willing. They put in a pathetic performance in the first half.
"His players are without doubt not performing at all so it wouldn't surprise me at all if he were to walk away."
Fellow pundit Danny Murphy said he believed the Dutchman would not quit the club.
"My worry for United is that whoever comes in they've got a squad lacking athleticism," said the former Liverpool and Fulham midfielder.
Sacked Chelsea boss Jose Mourinho and Bayern Munich coach Pep Guardiola, who is leaving his job in the summer, have been mooted as potential successors to Van Gaal.
Murphy said: "With Jose Mourinho you're guaranteed trophies and Pep Guardiola is the same. I'm sure there will be many meetings going on."
He added United could do "a lot worse" than give the job to assistant manager Ryan Giggs, who made 963 appearances for the club.
'Right decision on Rooney'
Van Gaal dropped Wayne Rooney to the bench at the Britannia Stadium.
The England striker, 30, came on for the second half but United still struggled to create chances as they went four top-flight games without victory.
Club captain Rooney has scored just two league goals this season and rarely looked like adding to that tally at Stoke, although he did set up Marouane Fellaini for a chance that was impressively saved by Jack Butland.
Shearer said the decision to drop Rooney was "a big statement".
Van Gaal said: "I thought it was the right decision, otherwise I would not have done it.
"We were better in the second half but then we didn't have anything to lose."