Karius, who joined Besiktas on a two-year loan deal this summer, has endured a horrible last few months.
Despite choosing to move him on over fellow goalkeeper Simon Mignolet, Karius insists he has a ‘great' relationship with the boss.
The German also explained his decision to move on from Anfield, citing first-team football opportunities following Alison's arrival from Roma.
“I have no problem with Jurgen Klopp, in fact we have a great relationship, he transferred me from Mainz,” Karius said, speaking to Bild.
“He never blamed me. The pressure got so big at some points from the media and the public that Liverpool had to react, which was not good for my situation, but that happens in football.
“Nobody told me to leave Liverpool. I didn't run away from Liverpool.
“I am at an age where I need to play regularly. After Alisson Becker's transfer I decided to move to Istanbul and join Besiktas.”
The 25-year-old's two mistakes against Real in Kiev proved costly, with the Reds enduring heartbreak and missing out on a sixth European Cup.
It was later reported that Karius was ‘concussed' after his collision with defender Sergio Ramos, however Karius says he does not intend to hide behind any excuses.
Instead, he looked to fellow countryman and legend Oliver Kahn, who suffered a similar fate in Germany's World Cup final in 2002.
“I don't know if he meant it or not. Only one person knows that: Sergio Ramos.
“I fell to the ground and thought to myself ‘what's going on?' I had adrenaline rushing through my blood and just wanted to play.
“But I don't want to hide behind any excuses.”
“I still can't explain the mistakes I made against Real Madrid. I have to get my confidence back and come to terms with the past.
“Oliver Kahn also made a big mistake in the World Cup final in 2002 and came back stronger.
“That is what I prefer to do rather than think about how long I will be haunted by the Champions League.”