Carlo Ancelotti accepted responsibility for Chelsea's dramatic slump after the 3-1 drubbing by Arsenal heaped further pressure on the Italian.
The champions have slipped from top of the Premier League to fourth place after going six matches without victory in the competition.
Ancelotti's position is now under intense scrutiny, but the Chelsea manager insisted he does not fear for his job.
"I don't know (how long owner Roman Abramovich will remain patient). Obviously he won't be happy at this moment," he said.
"I will take my responsibility, but this is a question you have to ask him, not me.
"I'm not afraid about my job. Everyone said I did a fantastic job last year. Now people are asking me about my job.
"We have to do better, obviously. It's not usual that Chelsea can't win for six games."
Arsenal climbed to second in the table after goals from Alex Song, Cesc Fabregas and Theo Walcott ended their five-match losing streak against their title rivals.
Branislav Ivanovic pulled a goal back for Chelsea, but it was a poor display from the champions and Ancelotti admitted his team must "wake up".
"I'm worried, obviously, because that's six games we've not been able to win," he said.
"I didn't see the team playing the way we want and we had difficulty playing our football."
"We're obviously not so confident playing in this moment. I didn't expect this defeat. I was surprised by this performance.
"I saw very good training sessions this week, so I was surprised by this performance.
"We are sleeping now. This is the reality of this team. We are sleeping.
"If you play against a good team like Arsenal, you lose if you don't wake up."
Ancelotti received support from Arsenal manager Arsene Wenger.
"I personally rate Ancelotti very highly and I can't believe that (his job would be under threat)," said Wenger.
It was a crucial victory for Arsenal, whose ability to compete against their main title rivals Chelsea and Manchester United has been doubted.
Wenger claimed the result has flooded his side with self-belief, and after leaking 13 goals in their last five meetings with the Blues, the Frenchman insisted they have developed some steel.
"This win has a double impact. Mathematically, it keeps us in touch with the leaders of the league," said Wenger.
"And psychologically, it was important. We were questioned about our capability of winning big games.
"I'm happy with the desire in the team. We kept good discipline in the team for 90 minutes and put in a real team performance.
"Two years ago with the same players, we were maybe battered by Chelsea. Last year we felt we were getting closer.
"This year, at United and Chelsea, we were more frustrated because we were more in the game and there was no real difference.
"Maybe we played a bit with the handbrake. It was a slow learning process that we got out of our system tonight.
"Cesc Fabregas said we were maybe scared to win. There was a strong word, but maybe there was something in it.
"We didn't see that tonight. It was a locked game at the start, but the first goal gave a huge advantage.
"We are not bullied any more, that is for sure.
"It's always very difficult to say because every game is different, but I feel we have matured over the last two years."
