Having been criticised for their performance during the midweek Champions League draw against Sevilla, questions were once again asked of the Liverpool backline when Scott Arfield put the Clarets ahead shortly before the half-hour mark.
Mohamed Salah quickly restored parity for the hosts, but they could not go on to find a winner despite having 35 shots and enjoying 71% of the possession.
"It feels strange, it feels wrong, but it is a fact we drew. A lot of parts of the game I was really happy with. We created moments but could not create in each one a finishing situation often enough. That is why I am still not in a perfect mood, I would say. Unfortunately I still don't feel any positivity in this moment. I am still in a 1-1 mood. It is easy to see the positive things [on Sunday]," Klopp told reporters.
"[The Burnley goal] was just a long ball. Trent [Alexander-Arnold] could have won the first header and the block on Joel [Matip, by Chris Wood] was difficult because the defender cannot do exactly the same because it is a foul. Raggy (Ragnar Klavan) was there to protect the situation but the ball bounced in the wrong direction and Robbo [Andrew Robertson] knows he could see Arfield quicker.
"It was a bouncing ball and [Burnley] were quicker. They are better in these situations, they are more used to it and he hit the ball perfectly but we could have defended much better. We conceded one goal and that is where we have to improve most, to switch the mood from being offensive all the time. We forget Mr Arfield and he can score. It doesn't feel good."
The result leaves Liverpool eighth in the Premier League table with eight points from their opening five games.