The summer signing recorded his first Premier League clean sheet for the Reds on Monday night as they were held to a goalless draw by Manchester United.
And while Klopp insists his compatriot can build further on his performances so far, the boss is comfortable with how Karius has fared between the posts.
He said of the ‘keeper: “[It is] a very good start, that’s how it is.
“We watched him for a long time and especially in the last two years in the Bundesliga, he was outstanding. But he is still a young boy, for a goalkeeper especially.
“He collected experience but this is, of course, something else here in the Premier League – a different kind of play in general in the Premier League and [a different] style of play in our specific case.
“So, of course, he has to improve and can improve, but with the start I feel quite comfortable and everything is good.”
Klopp continued: “It was not perfect. There was one situation [against United] with Dejan [Lovren] together, with passing, but things like this happen.
“More serious things like this happen to other goalkeepers who are more experienced. If you want a goalkeeper who plays football, you take the risk that sometimes the ball is bouncing in a different way.