The Chelsea defender was dismissed for rugby tackling Sadio Mane last man at the end of the first half yesterday.
VAR had to intervene after the Blues centre-half was initially handed a yellow card by on-field referee Paul Tierney.
The decision was overturned after he checked the pitchside monitor, though, and Chelsea failed to recover.
Mane bagged a brace early in the second half as Liverpool won 2-0 in west London, showing Frank Lampard’s Chelsea exactly what it takes to be Premier League champions.
Klopp, however, was far from happy with some unsportsmanlike behaviour on his bench during the game.
"Are you crazy? We never ever do that, ok?," Klopp could be heard shouting from the sidelines at a member of his staff when Christensen had to walk.
After the game, Klopp clarified the situation and said: “It was not one of my subs but another member of staff and I told him already what I thought and he is good with that.
"I am fine with that but in the moment it wasn't what I wanted to see.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
"I saw the sending off only in the situation. I saw Christensen's arms around Sadio so I thought in the moment it is a sending off but I couldn't see it back since then so if you have seen it differently, then I respect that.
"Would we have won it [if Chelsea had XI]? Who knows that! I thought we were good in the first half so I thought we could win it but if we would, I don't know.
"We know that it was a different game in the second half but I liked our first half already. I liked the way we tried to find solutions with the way we played. I liked the way we took on a difficult game.
"That was already very good and I was ready for a very positive half-time talk with a few pictures on what we could have done differently, where we have to move quicker, pass quicker, easier and stuff like this. Then, the red card, yes and it changed the game."
Liverpool overcame their first hurdle in their bid to defend their Premier League crown.
And their third top flight game of the new campaign comes next Monday when they face Arsenal away.
Chelsea, meanwhile, must bounce back in their bid to challenge for the title when they head to West Brom on Saturday.