Christensen was sent off shortly before half time after he hauled down Sadio Mane, who was clean through on Chelsea’s goal following an excellent pass from Jordan Henderson.
Referee Paul Tierney had initially given a yellow card for the foul before he reversed his decision after looking at the pitch-side VAR monitor.
As Christensen made his way off the pitch, Liverpool’s substitutes were applauding the decision.
But an angry Klopp turned to his Liverpool players in the stands and said: ‘Are you crazy? We never, ever do that, okay?’
Chelsea managed to get to half-time without conceding but Sadio Mane struck twice after the break to put Liverpool 2-0 in front.
Fikayo Tomori replaced Kai Havertz at the half-time break following Christensen’s dismissal.
Meanwhile, Thiago Alcantara was given his Liverpool debut for the full second half following an injury to Henderson.
But the £25 million signing from Bayern Munich gave away a penalty for a foul on Timo Werner, although Jorginho’s spot-kick was saved by Alisson.