The Reds were denied the three points in west London when second-half substitute Yoane Wissa converted for the Bees eight minutes from time.
The hosts took the lead in the contest through Ethan Pinnock before Diogo Jota quickly levelled with a clinical header.
After the half-time break, Mohamed Salah put Liverpool ahead with his 100th Premier League goal for the club, though Brentford responded when Vitaly Janelt netted from yards out.
Curtis Jones put Klopp's men back in front with a deflected, long-distance strike – but Wissa's clipped finish over Alisson Becker towards the end saw the points shared.
Read on for a full transcript of the boss' post-match press conference...
On the game and Liverpool's performance…
A wild, wild game. Offensively, I am really happy. I think in moments we played some of the best football we've played so far this season; we created top chances against a really well organised side. They were very good, but obviously we struggled tonight with their long balls. I was not too happy with how we started the game and that's how we conceded the goal, a little bit. It was a situation where we could have been more organised. It's not so easy, but [we needed] to be much more composed in this situation to win these little challenges. They scored at the second post; there was no space to score, but they did. We reacted well, scored really nice goals. The second half, we controlled the game better, but in the phase where we maybe played the best football, they scored the equaliser.
The 2-1 for Mo was outstanding; a super pass from Fab, who had so many good football moments. The goal from Curtis, outstanding, but because we didn't finish the game off the door stayed open and they used it again. They stayed in the game and it was really tricky for us tonight because usually when you play that well, you can control the game better but we couldn't because the goalie chipped one ball in behind always in our last line and they did really well with these balls – with the first and second balls – so you never can really control it and that made it tricky. They deserved their three goals and they deserved the point. I think we could have scored more; they could have scored one more, we could have scored four or five more and it would have been even more spectacular. But it's fine, we got a point, they got a point, let's carry on.
On the reason for substituting Jones for Roberto Firmino after his goal...
Obviously when we decided to make the change it was 2-2, but the reason for it was the way they played, we didn't really need a third midfielder because they only played long balls. So, we needed a clear structure around the centre-halves players who pick the ball up. When we did that, it made really sense that we had one more player between the line – changing our structure to give them another thing to think about. I actually think that worked really well. We didn't score from these situations but Bobby had a few really, really good situations passing-wise, keeping the ball all the time and stuff. We had massive chances – we had even in the last second a big one. Yeah, that was the reason. We thought we should score more goals to get the result we wanted.
On Salah scoring his 100th Premier League goal for Liverpool...
That's exceptional. I think two weeks ago he scored 100 in the league. Now 100 for Liverpool. We give him already the shirt with the 100 on the back – maybe we now have to give him another one. But exceptional, we all know that. In the future when people look back, people will speak about some players of this team 100 per cent and will speak 100 per cent as well about Mo Salah because the numbers he had are insane, incredible. But I know Mo and he is now in the dressing room and thinks about the two chances he missed. So, probably next time this will be the quickest player ever who scored 150 goals, that's the situation. But, of course, absolutely outstanding achievement, no doubt.
On what he made of Jones' performance...
Curtis is a top player. He is still a talent but a really, really good package and you felt that tonight. I thought he played a really good game. He won in the first half the best balls for us pretty much – he was really good in these situations. On top of that, he was involved in all football situations. He dropped in the right space, he was brave in between the lines, so many good things. But that's football – he's still young and consistency is then maybe sometimes a little bit of [an] issue. But in this moment he is in a really good moment and old enough to keep that moment going.