The German stopper has thanked Liverpool fans for supporting him after the game, while apologising for his performance on the night.
"Haven't really slept until now... the scenes are still running through my head again and again," Karius wrote on his Instagram page.
"I'm infinitely sorry to my team-mates, for you fans, and for all the staff. I know that I messed it up with the two mistakes and let you all down. As I said I'd just like to turn back the time but that's not possible. It's even worse as we all felt that we could have beaten Real Madrid and we were in the game for a long time.
"Thank you to our unbelievable fans who came to Kiev and held my back, even after the game. I don't take that for granted and once again it showed me what a big family we are. Thank you and we will come back stronger."
The 24-year-old joined Jurgen Klopp's side from Mainz 05 for £4.7m in 2016.