Chelsea boss Mauricio Pochettino has admitted that his job is at risk following the 4-2 defeat to Wolverhampton Wanderers.
After losing 4-1 to Liverpool in midweek, Pochettino would have been looking for a positive response from his side on Sunday.
The Chelsea head coach had reason to be optimistic when Palmer netted his 10th league goal of the season to give the Blues the lead inside the opening 20 minutes.
However, Wolves quickly hit back through Matheus Cunha, before an Axel Disasi own goal left Pochettino with work to do at the break.
Unfortunately for Pochettino, he could only watch on as Cunha added two more to his tally to complete his first Premier League hat-trick.
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Thiago Silva netted an 86th-minute header to pull a goal back, but it did little to lift the mood around Stamford Bridge with boos heard at the full-time whistle.
Speaking after Sunday's defeat, Pochettino conceded that "no one can be safe" amid speculation over his future as Chelsea boss.
"We are not good enough," Pochettino told reporters. "Myself, also. I'm responsible for this situation. What we showed today was not good enough.
"We didn't manage the situation properly and of course, no one can be safe. I don't want to come here and say I am the best. We're all responsible.
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"The players need to take responsibility like I take responsibility. At the moment we're not matching the history of the club. That's true.
"We need to accept it, be critical but we cannot give up. We'll work hard to change. If it's not working in this way, we need to move on and find a different solution."
Pochettino also apologised to the club's supporters following their first competitive home defeat to Wolves since losing 2-1 in March 1979.
The result moved Gary O'Neil's side into 10th position and knocked Chelsea down to the bottom half of the Premier League table.
Pochettino will have to quickly pick his players up ahead of Wednesday's away meeting with Aston Villa in an FA Cup fourth-round replay.
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