Jurgen Klopp's side have made it to the Champions League final for the second consecutive season and will face Tottenham in Madrid on June 1. Last season, they were beaten 3-1 by Real Madrid in Kiev, with Karius at fault for two of Los Blancos' goals.
And Alisson, who was in goal for Liverpool's semifinal opponents Roma last season, offered support to Karius.
Asked how he felt watching Karius' mistakes, he said: "I was saddened. We know the feeling of making a mistake in a competition as big as the Champions League; it's something that can stick with you for the rest of your career.
"But in life we always have the chance to make it better. I try to stay aware of everything. When I do something well, I don't let it get to my head. And when I make a mistake, I don't let it either."
Alisson joining as a replacement for Karius in the summer was pin-pointed as one of the main reasons behind Liverpool's improvement in form this season. But the Brazil international said he does not feel any extra pressure given Karius' mistakes -- and added that the responsibility is shared among the players.
"I don't think you can put it one guy's shoulders," he said. "The team has 11 guys.
"When we win, everyone wins. And when we lose, everyone loses. It wasn't Karius who lost that match, Liverpool did. This year we have a new opportunity, my first one.
"We will do everything to win and try to ease the pressure of being in the Champions League final."
Meanwhile, midfielder Fabinho said the Liverpool players are stronger because of their defeat in Kiev last season.
"We do not talk about what happened [in Kiev] in the dressing room much," he told ESPN. "I have not asked anyone what the days after the final were like either.
"But I think that having already played last season's final gives the team more experience. We already know the mistakes which need to be avoided.
"We are relaxed. It will be a different rival and our team is also different. We will do our best to win the final."
Information from ESPN FC's Eduardo Fernandez-Abascal