Karius replaced Alisson Becker with 15 minutes to go and given a passionate welcome by home fans after a difficult summer.
The hosts treated the fans to an entertaining match as goals from Roberto Firmino, Georginio Wijnaldum and Daniel Sturridge ensured they head into Sunday's Premier League opener against West Ham United on a run of four victories.
On Karius, Klopp stated afterwards: "It helps everybody. I haven't spoken to him because I was immediately in the signing session, if you want. I was not surprised, to be honest, but as a human being I was hoping for it, that it would be like this. I loved it, to be honest.
"Is it possible being different in a really hard world? Yes, I think it is possible. We showed tonight a really nice face and I liked it. It helps not only Loris, it helps Alisson as well, that you can see this is a very special place. It was a really big gesture."