Klopp's side endured a nightmare start to 2023 and they had only themselves to blame for the horror show in west London.
Ibrahima Konate's first half own goal set the tone for an evening scarred by mistakes at the back from Liverpool.
Yoane Wissa doubled Brentford's lead and although Alex Oxlade-Chamberlain got one back, Bryan Mbeumo wrapped up Brentford's first victory against Liverpool since 1938.
In his first appearance since playing in France's World Cup final defeat against Argentina in December, Konate took a large share of the blame for Liverpool's woeful defensive performance.
But the centre-back was far from alone in deserving criticism for a Liverpool display that left them in sixth place, four points behind fourth placed Manchester United who play their game in hand against Bournemouth on Tuesday.
Rocked by Liverpool's first defeat in five league games, Reds boss Klopp conceded Brentford's clever set-piece tactics were too much for his players to handle.
"Brentford create chaos with set-pieces. When I say they stretch the rules, they do, in offensive set-pieces," Klopp said.
"Don't get me wrong, it's smart, but they do. If you could single out all the situations you would find five fouls but because it's so chaotic no one sees it in the end."
Although seventh placed Brentford are on a six-game unbeaten run in the league, including an impressive win at champions Manchester City just before the World Cup, it was still surprising to see Liverpool torn apart so easily.
"You know before the game how strong they are from corners. The game got decided by the second goal which was our fault," Klopp said.
"We are not awake, they cross the ball and score the second that decided the game. The third goal should not have been allowed but we should have played better."
Darwin Nunez, signed from Benfica for £64 million ($77 million) last year, was another poster-boy for Liverpool's struggles.
The 23-year-old had 13 shots without scoring in his previous two league games and misfired again in the early stages.
Mohamed Salah's superb pass unhinged the Brentford defence and Nunez looked certain to end his barren run when he rounded David Raya.
But Ben Mee scampered back to clear his shot off the line as Nunez held his head in disbelief.
