Goals from Philippe Coutinho and summer signing Mohamed Salah gave the Reds a two-goal cushion in north London but Arsenal scored three goals in a frantic five-minute period to take the lead.
Granit Xhaka scored the second – his long-range effort was well-struck and moved in the air but should have been dealt with comfortably by Belgium stopper Mignolet.
Asked about the costly mistake, Klopp told Sky Sports: ‘He misjudged it. A second hand would have helped but that is how it is. You don’t need to make it bigger than it is.
‘It felt like we shouldn’t have conceded but we did. Defending is a team thing. Today we make individual mistakes and that is not cool.
‘My job is to think about the performance and that was a winning performance. If you want, the draw is our halfway win. We are always a better side when we draw. We have to take the good things and work on the lesser good things.’
Despite Arsenal taking a surprising lead during the second-half, Liverpool earned a point as Roberto Firmino found the back of the net with another strike that should have been saved, this time by Petr Cech.
On his team’s overall performance, Klopp said: ‘You need to be angry with yourself, not sad or insecure.
‘We came back into the game and scored our third. The point is the minimum we deserve. Because of the intensity of the game it was not easy to create clearer chances.
‘When you get a point at Arsenal it is usually OK but after this give me a few minutes to get there. Three goals at Arsenal should be enough.
‘We defended most of the time pretty well. We did not give space away. After they score the first and the second, it is not easy but we need to deal with these situations better.’
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