Graham Potter pleaded with his Chelsea players to "stay together" after a shock 2-1 defeat at Fulham that saw Blues forward Joao Felix sent off on his debut before a decisive blunder from Kepa Arrizabalaga.
Potter's troubled side crashed to a seventh defeat in their last 10 games in all competitions after another spluttering display.
Chelsea fell behind to a goal from their former winger Willian in the first half at Craven Cottage on Thursday.
Kalidou Koulibaly equalised after the break but Felix was dismissed for a reckless studs-up lunge on Kenny Tete.
Fulham were gifted their late winner by Chelsea keeper Kepa, who made a hash of dealing with a cross that Carlos Vinicius converted to leave Potter facing renewed talk of the sack just four months after he replaced the axed Thomas Tuchel.
"We made a couple of mistakes for their first goal, then the red card changes the game. Disappointed with the second goal because I think we could do better and that is what cost us," Potter said.
Potter this week labelled managing Chelsea as "the hardest job in football" after a turbulent period that is severely testing owner Todd Boehly's faith in the former Brighton boss.
Chelsea are languishing in 10th place – 10 points adrift of the top four – after their wretched run extended to one win in their last nine league games.
They have managed just four goals in their last eight games in all competitions and Potter desperately needs a victory against Crystal Palace on Sunday to buy himself at least a little breathing space.
"We have got to keep working. There is no other solution. You have to keep working, stay together and try to get the three points," Potter said.
Hampered by a debilitating injury list, Potter held a meeting with senior players Cesar Azpilicueta, Thiago Silva, Jorginho and Mateo Kovacic on Tuesday in an attempt to calm the crisis.
But Chelsea fans' patience is already wearing thin and losing to sixth placed neighbours Fulham was another bitter blow to his hopes of avoiding the sack.
It was in keeping with Potter's misfortune that Felix's promising debut ended prematurely after his loan move from Atletico Madrid on Wednesday.
"It was a forwards tackle. There was no malice in it but I understand why it was a red. It is another blow. The hits keep coming at the moment," Potter said.
The 23-year-old Felix, who cost Chelsea a reported 11 million euros ($12 million) loan fee, was one of four changes from the 4-0 FA Cup defeat at Manchester City last weekend.
Given license to roam across Chelsea's three-man attack, Felix's pass found Kai Havertz and when the German's shot was blocked, he laid the rebound to Lewis Hall, whose low drive was saved by Bernd Leno.
Picked out by Mateo Kovacic, Felix fired wide from the edge of the area, then volleyed over after Azpilicueta's cross found him unmarked 10 yards from goal.
But Potter was left to rue dreadful defending when Fulham took the lead in the 25th minute.
Hall surrendered possession and Chalobah failed to clear properly before Willian unleashed a powerful drive that took a deflection off Trevoh Chalobah as it flashed past the wrong-footed Kepa.
Potter was ashen-faced on the bench as Fulham fans taunted him by singing "Stamford Bridge is falling down" and "you're getting sacked in the morning".
Chelsea were level two minutes after half-time as Mason Mount's free-kick hit the post and rebounded to Koulibaly, who stabbed just over the line before Leno could save.
But even then, Potter's luck wouldn't last as Felix saw red after needlessly throwing himself into a high tackle that crashed into Tete's shin.
There was an even more ignomious contribution to Chelsea's downfall from Kepa in the 73rd minute.
Kepa completely misjudged the flight of Andreas Pereira's cross, allowing it to sail over his head to Vinicius, who nodded into the empty net while Chelsea defender Thiago Silva screamed at the hapless keeper.