The Premier League champions were involved in a tightly contested first half at Stamford Bridge but the game changed when Sadio Mane was put clean through on goal by Jordan Henderson only for Christensen to haul him down.
Referee Paul Tierney had initially given a yellow card but, after consulting VAR and looking at the pitch-side monitor, he decided to upgrade the punishment to a red card.
Liverpool’s bench had been animated when Mane was brought down and felt Christensen was the last man, with a staff member applauding as the dismissed centre-back walked past the bench and down the tunnel.
When Klopp spotted that he was livid, yelling in the general direction of the bench: ‘Are you crazy? We never ever do that, okay?’
Asked afterwards what had had happened, and whether it was a player who has been applauding, Klopp explained that it was a member of his coaching team.
‘And I told him already what I think about it and it’s good with that, I’m fine with that.
‘But in the moment, yeah, it’s nothing I want to see.’
With Chelsea down to 10 men in the second half, Klopp opted to bring on new signing Thiago Alcantara at half-time and the Spaniard gave an excellent display as Liverpool dominated the rest of the contest.
Mane was the decisive factor in the match, scoring a header shortly after the restart before capitalising on a mistake from Kepa Arrizabalaga to double the scoreline, while Chelsea missed a late penalty to get back into the game.