Claudio Ranieri does not know if his job is under threat after a damaging 2-0 defeat at Southampton pushed Fulham closer to Premier League relegation.
The Cottagers slipped a perilous 10 points adrift of safety at St Mary's, with under-pressure manager Ranieri subject to protests from the travelling fans.
First-half goals from Saints duo Oriol Romeu and James Ward-Prowse inflicted the London club's seventh defeat from eight top-flight games.
Asked about his future, Ranieri replied: "My job? I don't know. Ask the owner."
Chants of 'You don't know what you're doing' greeted Ranieri's second-half substitutions, while a banner containing the words: 'Risk free? Are you watching Tony Khan?' was unfurled in reference to comments made by the club's vice-chairman following the Italian's appointment in November.
Ranieri, who said he may speak to Fulham owner Shahid Khan on Thursday, insisted he will continue to fight for an unlikely great escape with 10 games remaining.
"Something could happen. If you don't believe, it's done," he said.
"You have to believe. You have to fight. If you don't fight, already you've lost.
"Always in my career, I'm used to work hard. I know it's very difficult but until mathematically it's impossible we continue to fight."
Second-bottom Fulham were comfortably second best on the south coast and, aside from Ryan Babel rattling the crossbar late on, offered little response to their two-goal deficit.
Despite the performance and result, Ranieri was adamant his players gave 100 per cent effort.
"The disappointment is very, very high because every time the opponent shoot at goal they scored a goal. It's unbelievable. This season many times it happened and also tonight," he added.
"I think when this happens, the confidence goes down.
"We tried to do our best but that's it, the maximum my players can do."
Southampton boss Ralph Hasenhuttl hailed the victory as a big step towards safety after his side climbed out of the bottom three by ending a four-game winless run.
With Fulham and bottom club Huddersfield cut adrift, the Austrian believes his team are now competing to avoid the other relegation place.
"If you're under the line then you're gone so it's about this one position and I think it's a battle between five or six clubs," he said.
"We are one of them and, at the moment, we are over the line and it's important for the mentality factor because we know the next two games (Manchester United and Tottenham) it's not so easy to take points.
"I was speaking before the game how important this is for the whole club and I think we felt a special atmosphere in the stadium, it was fantastic supporting from the first minute on.
"It was a win for the whole club, I think it was a big step for us - only one, but a very important one."