A frenetic game between the league leaders and the champions ended 2-2, with Sadio Mane and Mohamed Salah’s leads for Liverpool cancelled out by Michael Keane and Dominic Calvert-Lewin.
Liverpool thought they had snatched a late winner only for Jordan Henderson’s effort to be ruled out by VAR by the meanest of offside margins on Mane.
The home side had Richarlison sent off late on for a dangerous lunge on Thiago Alcantara but goalkeeper Jordan Pickford was lucky to escape a sending off himself earlier in the game for a bad tackle on Virgil Van Dijk, who went off injured.
Klopp was impressed with Liverpool’s performance on the day but was left disappointed by some of the decisions that did not go his side’s way.
"The performance was top. A good game from both teams," Klopp, who on Saturday also celebrated the fifth anniversary of taking charge of his first Liverpool match, told BT Sport.
"We were clear, dominant against a side that is full of confidence. We played a really good game, probably the best away game since I am at Liverpool, playing at Goodison. In the end it's 2-2 for different reasons."
On Pickford's tackle that forced Van Dijk off injured, Klopp said: "I didn't see it back, it took a while so obviously the offside was not too big and Pickford kicks him completely.
"Then the Henderson goal, it was the pass for Sadio, and I didn't see offside. Maybe somebody can explain it to me. The picture I've seen was not offside.
"It's difficult at the moment. The red card for Richarlison is not only a red card for Everton, it's a massive foul on Thiago and [his injury] looks not good.
"The game is over, we've only got one point, maybe we should have more, but we cannot change it. The game was good, I loved it, a really good game.
"The [Everton] second goal is an individual thing. Calvert-Lewin is an incredible player, that's all he had to do and he did it, apart from that we dominated it. Both teams get the point."
