Goals from Mohamed Salah, Diogo Jota and Curtis Jones had cancelled out earlier strikes from Ethan Pinnock and Vitaly Janelt and looked to have secured Liverpool the win but Brentford came back again to earn a point.
"We did our bit. We played really good football, created incredible chances. We scored three, should have scored four, five, six but they deserved their three goals and could have had four. They did very well and that's why they deserve the result," Jurgen Klopp said after the match.
"The atmosphere was incredible and they fought really hard. We fought as well. But we have to be ready for a proper fight because they make a fight of it. We were, but we lost too many challenges in the air and that lost us momentum."
It was Brentford who got the scoring underway first with Pinnock sliding in at the back post off a free kick on 27 minutes to send them in front.
However, it took Liverpool just four minutes to equalise when Jota got on the end of a Jordan Henderson cross which he headed into the goal.
The teams were level going into the second half but Liverpool dominated possession and were rewarded early on when Salah volleyed the ball into the net on 54 minutes to bring his all-time Premier League goal tally to 102.
The assistant referee flagged for offside but VAR overturned the decision and allowed the goal.
Despite seeing little of the ball, Brentford took their chances when they came and Janelt headed them level on 63 minutes from close range.
It was another cross that caught Liverpool out in the final 10 minutes as Wissa chipped the ball over Alisson to level the score.
"We played brave with big determination throughout the game. Second half, when they went 2-1 up, we stayed in the game and then in the end we maybe could have won the game. I felt at times it was a little bit too open but we need to look into that," Brentford manager Thomas Frank said.
"Very, very pleased that we were able to score three goals. A lot of teams haven't created many chances against them. We managed to capitalise today and I'm very pleased with that. We tried to play, to attack. I believe if you play offensive and if you are attacking there's a bigger chance to get a result."