Klopp joined fullback Andrew Robertson in animatedly confronting referee David Coote and the match officials after the final whistle.
The left-back had been denied a penalty when challenged by Burnley's Johan Gudmundson during the second half.
“I spoke about the goalkeeper situation," said the Reds boss. “How can you let it happen constantly that the goalie has three players allowed to block him?
“It's just not how it should be. For the referee it wasn't a foul and he didn't whistle.
“It had no influence on the result though, as I realised later."