Sunderland’s victory allowed them to escape the relegation places and they sit in 17th on 32 points having played a game less than the current bottom three of Norwich City (32), Fulham (31) and Cardiff (30).
Fulham next face a trip to 10th-placed Stoke City on Saturday before finishing their campaign at home to Crystal Palace, who are 11th.
“I think we need to win the last two,” Fulham defender Brede Hangeland was quoted as saying by British media on Monday.
“That is clear for everyone to see. Is that impossible? No, it is far from impossible. Of course we can do it.
“It is all about doing the business next week and then the week after and hoping that will be enough. It is a massive game next week and we have to win that.”
Fulham have conceded a league-worst 79 goals in a calamitous campaign with German Felix Magath their third manager of the season and struggling to arrest the slide.
The German replaced Rene Meulensteen in February after the Dutchman was sacked following a run of defeats despite being backed heavily in the January transfer window.
Greece striker Kostas Mitroglou has played only twice after struggling for fitness since joining for around 12 million.
Magath, though, was focusing only on next week’s fixture as Fulham attempt to secure a 14th consecutive season of top flight football.
“I am not afraid we won’t stand up for the next game,” he told the British media.
“We still have a chance and will go on and try to take it. We were in front and everything was fine and then they get two goals it seemed like it was the end of the season.
“The players were very disappointed in the dressing room and they didn’t talk. I told them it’s too late now, we have to stand up and take our chance if we get a chance next week and try to win at Stoke.”
Cardiff face an even bleaker situation as they sit bottom with a trip to Newcastle United to come before a final day clash at home to a title-chasing Chelsea.
The Welsh side have the second worst defence in the league behind Fulham and have also changed managers this season with Ole Gunnar Solksjaer brought into replace fan favourite Malky Mackay, who led the team to promotion last year.
Cardiff were as high as 11th after beating Fulham early in the season but a public spat between Malaysian owner Vincent Tan and Mackay was followed by a slide down the table with the Scot eventually sacked in late December with the team in 16th.
Former Manchester United striker Solskjaer has managed only three league wins since taking charge, but still believes they can avoid the drop despite a joint-worst record of seven victories in the campaign, shared with West Bromwich Albion who are 15th on 36 points, one ahead of Aston Villa.
“We thought we needed two wins before today,” the Norwegian said after the Sunderland loss.
“Now we’ve got two games left and we’ve got to win them. It’s hugely disappointing and of course we’ve taken a big blow but we won’t give up.”
(Writing by Patrick Johnston; editing by Amlan Chakraborty)