The two-time Champions League winners, who also won the English title five times between 2005 and 2017, are having a second disappointing season, two years after a US-led consortium took over the club and invested heavily in players.
Watching their side throw away 1-0 lead to go 2-1 down mid-way through the second half was too much for some of their supporters in the away end at the Brentford Community Stadium.
First came the shouts of "Roman Abramovich, Roman Abramovich" as fans sought to contrast their successes under the club's former Russian owner with their mid-table position now.
Then came a vitriolic chant about Todd Boehly, the most prominent face of Chelsea's new ownership, another celebrating former manager Jose Mourinho who won three league titles at Stamford Bridge and finally a crude one about Pochettino, the former Tottenham Hotspur manager.
Other Chelsea fans sought to rally behind the team who eventually battled back to secure a 2-2 draw when defender Axel Disasi forced in a header in the 83rd minute.
"It is normal. We were losing the game 2-1 and it's about expressing frustration," Pochettino told reporters.
"Of course we are responsible. I am one of those responsible, I am the head coach."
He said Chelsea's management team needed to earn a better relationship with the fans by winning more games but he also said: "We need to manage some reality."
The Argentine has previously said it is unrealistic to compare Chelsea now, after an overhaul which saw a string of young and relatively inexperienced players join the club, with the triumphant teams of the recent past.
"We are working really, really hard to win games and the team is fighting," Pochettino said.
He also said the side was tired after playing 120 minutes in the League Cup final that they lost 1-0 to Liverpool last Sunday and then beat Leeds United with a last-gasp winner in a 3-2 thriller in the FA Cup on Wednesday.
"I am fighting with all my sense to try to provide the team with the best tools to work and improve and to play in the best way," Pochettino said.
"Today is my 52nd birthday. I know very well this business. But I know we're never going to give up. We're going to fight."
