The 24-year-old gifted Karim Benzema the opening goal of the game, before failing to catch Gareth Bale's long-range shot that secured a third successive Champions League trophy for Zinedine Zidane's side.
The German keeper had not made a single error in the competition prior to the final, but still feels responsible for Liverpool's defeat in Kiev.
"I don't feel anything right now," Karius told reporters after the game.
"Today I lost my team the game and I feel sorry for everyone - from the team, from the whole club - that the mistakes cost dearly. If I could go back in time I would. I feel sorry for my team. I know I let them down today. These goals cost us the title basically. It's very hard right now but that's the life of a goalkeeper. You have to get your head up again.
"Of course everyone tried to cheer me up. But there was just silence everywhere because everyone was really disappointed."