Karius clumsily threw the ball into Karim Benzema's path for the opener and failed to catch a seemingly straightforward effort from Gareth Bale that made the score 3-1 and put the game out of Liverpool's reach.
Talking after the game, Klopp said: "What can I say? Loris knows it, everybody knows it. It's a shame in a game like this and after a season like this. I really feel for him; he's a fantastic boy."
"Nobody wants that, [but] that's the situation. The mistakes were obvious, we don't have to talk about that, its all clear; he knows it, I know it, you all know it.
"Now, he has to deal with it, we have to deal with, we will do that, of course, we will be with him, there's no doubt about that. It was not his night, obviously."
Karius was captured in tears after the game, consoled by man of the match Gareth Bale. The German spoke to 'talkSPORT' and held his hands up for his errors: "I don't feel anything right now. Today I lost my team the game"
"I feel sorry for everyone. I'm sorry for everyone, for the team, for the whole club. The mistakes cost us dearly.
"If I could go back in time I would. I just feel sorry for my team. I know I let them down today," said Karius.