The 237th Merseyside derby ended 2-2 after Jordan Henderson's injury-time finish was ruled out for offside by the video assistant referee.
Sadio Mane had given Klopp's side the lead with just three minutes on the clock before Michael Keane made it 1-1 midway through the first half.
Mohamed Salah scored his 100th goal for the Reds in the 72nd minute, though Dominic Calvert-Lewin's towering header restored parity not long after.
Everton were reduced to 10 men as a result of Richarlison's heavy challenge on Thiago Alcantara just minutes prior to Henderson's goal being chalked off.
Read on for a summary of Klopp's post-match press conference...
On the drama at the end of the game...
It's getting harder and harder to take it, to be honest, because I went in the dressing room after the game, I liked the game, really good game from my boys. It was the best away derby we played since I am at Liverpool – top football, conceded goals because of the specific strength of Everton. The set-piece was unlucky when they scored, so Virg is not on the pitch and we have to sort that. We sorted it in the game, the only problem was that was, I think, the first corner after he left the pitch, so there was this little moment of disorganisation. They used it – that's [the] quality of Everton. The second goal, we avoided pretty much all situations like this over the 90 minutes but one time we let Digne cross. I heard already when the ball was in the air from the Everton bench, 'That's it' because they know he is really strong in these situations and he scores that goal. Good goal. Our goals were brilliant.
Then I leave the pitch and Thiago tells me that in the red-card situation with Richarlison he thinks he got injured. We will see if it's true or not. If a player felt like this, we need to have a look. Then I come in the dressing room and people stand there with a laptop and other people stand around the laptop and I asked what's on. They say, 'We watched the situation back and we don't understand why they whistled offside.' Look, I'm a real supporter of VAR but you would expect that, especially with offside, you then do the right decision. We scored a goal one time at Aston Villa and they said the armpit was offside – sounds funny, we got it. This time, the picture I saw now once on the laptop, there is no armpit, there is nothing, we are just not offside. Since then I had 10 interviews around about and everybody tells me it was not offside and that doesn't lift my mood obviously. You all watched it obviously more often. That's tricky. We lost a player in a situation where VAR was not involved with Virgil and then maybe another one in the red-card situation and scored a legitimate goal – whatever the word is – which didn't count. So, obviously not our day but the performance was the performance I wanted to see.
On Salah bringing up 100 goals for Liverpool...
Unfortunately, I hope you find something in your notes about how often I said how good Mo is and all these boys are great. The goal – sensational. But I am not in the mood to talk about that now. Yes, it was a sensational goal and the numbers are incredible, it's really crazy. But not even Mo wants to talk about it in the moment.
On Jordan Pickford's challenge on Virgil van Dijk in the first half...
In the game, it was pretty quick. For me, it was a clear penalty what I saw and then obviously we saw that the flag went up, so offside. I still thought it's worth to have a look on the foul but that didn't happen. We have no power there, we just sit here and now you discuss it with me. We have to ask other people about that. What can I say? I don't want to say Jordan Pickford wanted to do it but it's, of course, not a challenge how a goalie can do it in the box because there's another player. If it's not offside, it's 100 per cent a penalty. So it's nothing, that's all.
On the team's reaction to the Aston Villa defeat prior to the international break...
How I said, it has nothing to do with my message two weeks ago how the boys played today. These boys are exceptional, these boys are a team. I am 100 per cent of the time proud of being their manager. Yes, in Aston Villa we played an under-average game, a bad game and then you lose in the Premier League a game. We lost 7-2, that doesn't happen too often. I'm not surprised about the reaction, that’s what I wanted to see but it's still only a draw. But the game, the performance and the reaction, I think everybody who is with us thought today that was pretty good. You know Everton is in a sensational moment, really flying, winning the games and all this stuff. Then getting dominated like they got dominated here today at home, I think that's not easy but my boys did it today even in very, very difficult circumstances – just losing a main player very, very early. Joe Gomez played a sensational game. I think everybody thought, 'Chip the long balls, Calvert-Lewin.' Gomez dealt outstanding with it. I liked it a lot. Good game, same old result.
On the confidence of the squad...
How I said, I am not worried about the boys. The problem that we have in the moment is just I am really not in a good mood because, how I said, you all gave me the same information. We should have won the game, we didn't and I have injured players in the dressing room – that's not good. We will see how we will respond. We will show the response we can show in other situations, and we scored today a late goal but it just didn't count for some reason. So the boys are fine in that but [couldn't] make the decision if it counts or not. Would you have asked the same question if the ref would have said it was not offside? It's all the same.