Alex Oxlade-Chamberlain scored within two minutes to cool any nerves in the away end, before doubling the advantage with a fine first-time finish.
Speaking to BT Sport, Klopp said: "There were good moments. 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."