Pochettino's side dropped into the Premier League's bottom half following another heavy loss, four days after being beaten 4-1 by leaders Liverpool.
"We are all not good enough at the moment, that's the reality," he said.
"Myself also. I'm the first responsible for the situation. What we showed today was that we are not good enough."
Argentine Pochettino, 51, took charge of Chelsea in July following a season in which they finished 12th under interim manager Frank Lampard, after Graham Potter and Thomas Tuchel were both sacked earlier in the campaign.
The Blues, five-time Premier League and two-time Champions League winners, have the same number of points at this stage of the season as they did after 23 games under Potter last term and were booed at full-time on Sunday.
Former Paris St-Germain and Tottenham manager Pochettino said it was "a matter of time" before his young squad begin to show sustained progress - although he accepted "patience is not infinite".
"We didn't manage the situation properly. No-one can be safe. I don't want to come here and say I am the best and the players the worst," Pochettino said.
"I think we are all responsible. But the players need to take responsibility also.
"At the moment we are not matching the history of the club. We need to accept that and to be critical but we cannot give up."
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