The Reds were held by the current Premier League leaders but went close to breaking the deadlock through Roberto Firmino on two occasions in the first half.
However, Alisson Becker ensured Klopp's men left L4 with a point as he made fine saves to deny Bruno Fernandes and Paul Pogba towards the end of the second period.
Read on for a transcript of the boss' post-match press conference...
On whether he felt it was a point gained or two dropped…
We have a point more than before the game. I think the performance was good enough to win it but to win a game you have to score goals and we didn't do that. That's why we have that result and it's absolutely OK.
On whether Manchester United are the most threatening they've been during his time as Liverpool manager…
I don't think in these categories, they were always a threat in the moments when we met them. They were always good, they were always organised, sometimes a little bit under pressure for the wrong reasons and all these kind of things. It was always a threat and always difficult and that's never changed. I am not sure if it's more or less, in that moment it is just how it is.
On going three Premier League games without scoring…
No, there is nothing fundamentally different, it's just the result is different. We try and we don't score or we try and we score – that's a big difference, to be honest. [Jordan Henderson] is right, we have not to worry about it but obviously we work on it. It's not that we ignore the fact and just hope it will be good again. We did that but the only possibility you have to score goals is to create situations and to be ready to fail and to do it again. That's a massive difference between when you are flying and you score with pretty much each chance you have because then you deal with the missed chances better. It is just information. That is the difference and nothing else. I saw my team playing tonight and I saw a really good football team with a clear idea, with super passes, great counter-press and great desire to score – but we didn't score. We will create chances and we will score, but I know, now we face Burnley on Thursday and they are not famous for conceding an awful lot of goals. Then a few days later we play again against United and they obviously defend with all they have. It is not that we just decide from now on we want to score again and now we will do it, but I see the boys really in the situation and I will help as much as I can so that we change it as quickly as possible.
On this season's battle for the top four...
I knew it always. That's always clear. In the season when we came second, the day when I started really thinking about the title race was the day when it was clear that we are in the Champions League. I know my job and I know what I have to do. The most important thing is to qualify for the Champions League and I know how difficult it is. Yes, you are right. This season will be a tough race for the top four. True.
On Jordan Henderson and Fabinho's performances at centre-back...
Playing on top of that really good football, made our build-up really flexible, made it really difficult for United to press – I can't remember a real pressing situation of United and they are pretty good in that actually. So, that was really good, absolutely.
On how he looks at Liverpool's situation in the Premier League...
I cannot decide how you look at it, to be honest. I have no idea and I cannot decide how people look at it. I know that football fans in general are not the most patient species on this planet, so they want to win each football game. I'm not too different to that but I am long enough in the business to know that you have to go through more difficult periods as well. It's not the most difficult in my life – not even close to it. So it's just a situation where we play football and have had injuries, still have injuries but got used to the injuries we had in the long term and now players coming back and all that stuff. So, Thiago played today a great game, a really good game, and I think it was his second start for us, so there's space for improvement like how we work together and all these kind of things. For me it's not too important where we are in the moment, it's important that we have points and we are around this group. We spoke about the fight for the Champions League, so that's the most important thing and for that you need points. We have them and we are in the middle of a group of teams which fight for this spot and that's what we have to do. That's the job. It's not about, 'If we don't become champions, it's not fun anymore.' That's not like it is. We just fight for everything and I saw that tonight again. That's all I need.