Karius, 25, joined Besiktas on a two-year loan in August, a month after Liverpool signed goalkeeper Alisson from Roma for £56 million.
His mistakes in the 3-1 defeat, which he has said resulted from concussion after he was elbowed in the head by Madrid's Sergio Ramos, led to criticism that he said he struggled to deal with for some time.
"It was a super season with a very unfortunate end, but you must get over it," Karius told Bild. "I knew that I must get up again and not hide and only concern myself with the past. It was a super team performance to just reach the final. Nobody can take that away from me. Not many German keepers can say they've played in a Champions League final.
"A lot of things came together that day, and even though nobody wants to hear about it, you will never know how much my mistakes were connected to the injury which was diagnosed later. That's no excuse -- just an explanation."
Karius said he does not know and "does not care" whether Ramos' elbow was intentional, and while Ramos did not apologise for his actions, he does not hold any ill feelings toward the defender.
In fact, he said he watched the clip of the incident several times to try to learn from it, because "for one [or] two weeks, it was on my mind every day."
"You sometimes don't understand how a situation like that can happen," he said. "I wanted to understand it better and that's why I watched everything again that night and the following day."
When Liverpool signed Alisson in July, shortly after he finished representing Brazil at the World Cup, it was seen as a lack of belief from the club in Karius.
But Karius said manager Jurgen Klopp was in contact with him the entire time and told him the decision was not personal.
"Jurgen Klopp called me several times during my holidays to build me up," Karius said. "Nothing stands between us. He never blamed me [for the defeat]. But the pressure in the media and the public increased and Liverpool had to react. It wasn't a good situation for me, but things like that happen in football."
Because of the way Liverpool conveyed the news of Alisson's signing, and also how they handled his request to leave the club afterward, Karius said he and Klopp remain on good terms.
"We have a good relationship," Karius said. "He signed me from Mainz. I could have also stayed at Liverpool and played a few matches, but I wanted to be No. 1 [somewhere] and get regular game time.
"Nobody told me that I must leave. It was no escape from Liverpool. I still have a good relationship with the people there."
Karius also said he knows questions about his quality will continue to be asked, but all he can do is try to answer them and succeed with Besiktas.
"I can't undo it," he said. "It's in the past. It's over. Oliver Kahn also made a big mistake in the 2002 World Cup final and came back stronger. I'd rather focus on that than think about how long the Champions League final will still be with me. I want to put it behind me instead of bottling up everything."
