Alex Oxlade-Chamberlain scored the Reds first two goals on the night, marking his first Champions League start in 18 months in style, before Sadio Mane and Mohamed Salah added two more late on before a late consolation from the hosts.
Liverpool lost all three of their group stage games last season, only edging through before going on to win the trophy, the first under Klopp.
But the German wasn’t entirely happy with his team’s performance on the night.
“There were good moments,” he said, speaking to BT Sport.
“The start was brilliant, we were kind of fluent and asked them a lot of questions but then we started – I’m not sure why – to lose patience and some easy balls. But all four goals were brilliant and we had chances to score more. Job done.”
“In the years before we would have drawn it, maybe even lost, but all’s OK. It was intense, we needed concentration. Our opponent brought in their tallest player and they did well from the first and second balls.
“We played with speculation when do we really need to go there? Then they won the second balls. So I didn’t enjoy the game too much, but I enjoyed the result.”
Liverpool remain second in Group E, one point behind Napoli, who beat RB Salzburg with a 3-2 away win.