Mohamed Salah's goal against his former club looked set to restore Liverpool to winning ways after their calamitous 3-3 draw against Sevilla, only for Willian's mishit cross to earn Chelsea a point.
The German also played down talks of the title for now. "In our situation, if we would really think about [league leaders] Manchester City we would be crazy," said Klopp, whose side had let a 3-0 lead slip against Sevilla in mid-week. "How can we get Manchester City? We have to win games, but if they go on winning all their games, we can do whatever we want."
The German had no complaints with his side despite them dropping two more points at home.
"I'm happy about big parts of the performance," he said. "I'm really proud of the attitude. Everything was good until Willian crossed the ball. The world is in a strange, crazy place at the moment and there are much more important, crazy things that are happening. I can easily live with a point against Chelsea."
Willian struck two minutes after coming on for Davide Zappacosta, drifting across the box from left to right before lifting a cross towards the back post that dropped beneath the crossbar.
Klopp had been trying to send on the fit-again Adam Lallana in order to change to a back three and said he was mystified by referee Michael Oliver's initial refusal to allow the change to take place.
"In my mind, Ragnar Klavan would have been in exactly the position where Willian crossed the ball," said Klopp. "That means we would have blocked the cross. So you don't feel too good when the ref doesn't allow you to change the system because he thinks maybe it's time play [wasting] or something. I've no idea why he said no."
Klopp said Chelsea had played more defensively than he had expected and summarised their approach as: "Deep defending and giving the ball to Eden Hazard."
But Chelsea manager Antonio Conte felt his team had "dominated" the second half and said Liverpool's goal — tucked away by Salah following a loose touch by Tiemoue Bakayoko — had also been fortunate.
Asked if Willian's lob had been deliberate, Conte smiled and said: "It's not important. It was important to score. "But at the same time I think that we conceded the first goal in an unlucky way. It was a fair result, but in the end I think that we deserved a little more than Liverpool."
Although his influence faded, Hazard was Chelsea's stand-out performer, his every touch in the first half oozing sophistication.
"The start of this season was full of trouble with Eden because he had an injury with the national team and then we started the season without him," said Conte. "[But] now Eden is in really good form. He likes to play as a striker. There is a good link with Alvaro."
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