Keane Lewis-Potter headed Brentford in front just before half-time, but Yehor Yarmoliuk was dismissed for violent conduct in stoppage time. Victor Muñoz equalised after the hour before Alexander Isak completed the comeback, with captain Vitaly Janelt sent off late on for a second bookable offence.
Liverpool manager Andoni Iraola believed his team had earned a valuable result against difficult opposition.
“I think they are a very important three points for us because I think it's very expensive to win here. I think Brentford are a very good team, especially at home, and to finish with three points here is very valuable,” he said.
Iraola was pleased with Liverpool's patience against ten men, particularly before Isak's winner, but felt his side became less assured after taking the lead.
“I think we played really well the minutes up until we scored the 2-1 against 10 players. I think that we were being patient and we were finding good positions and we were in control of the game really well,” he said.
“Probably more disappointed after we scored because you scored the 2-1 and then you feel like you have something to lose.”
The Liverpool manager also questioned the decision to overturn a first-half penalty after VAR intervention, arguing that the contact following Dango Ouattara's touch of the ball did not justify the technology becoming involved.
Brentford manager Keith Andrews was proud of his team's overall performance but accepted that the dismissals had changed the contest.
“The overall feeling is I'm filled with a lot of pride around what we are, who we are, how we do things overall. I felt it was a pretty even game. I thought we were gaining momentum and confidence within the game and wanted to create a faster game,” he said.
“Second half changes the momentum of the game and it proves more difficult.”
Andrews felt Yarmoliuk had been drawn into reacting to an opponent, although he acknowledged his midfielder should have handled the situation better.
“I think Jacquet is very clever, he walks towards him when the ball is the opposite way. I think he's in a state of trying to provoke. I don't think Yarmo reacts in as good a way as he should,” Andrews said.
Liverpool's attacking options also made a difference after the break. Iraola praised Bradley Barcola for repeatedly getting into dangerous positions despite missing chances, while highlighting the creativity of Florian Wirtz, Rio Ngumoha and Muñoz against a defence protecting its penalty area.
Brentford's manager was left to reflect on a match in which his side had competed strongly before losing control of the numbers.
“Disappointing because we're a team that feels we can go toe to toe with any team,” Andrews said. “When it's an even keel we're in a good place and we gave them an advantage.”