The Reds moved clear at the top of the Premier League table by continuing their 100% start to the top-flight season with a home win over the Gunners on Saturday evening.
Liverpool are yet to keep a clean sheet this season and, despite the marked step up in standard of overall performance, Klopp believes their game management can still be better.
“If we could have controlled the game better, that remains our real challenge," said the Reds boss.
“It doesn't happen often but if it happens when you are 3-0 up or 4-0 against Norwich... Arsenal didn't really press any more. They were deep and together, and we kept passing the ball to their legs. It made no sense.
“The last 10 minutes I saw the possession - 53 to 47 or something like that - but over 80 minutes it must have been completely different. For 80 minutes we were completely in charge of the game. We are not Disneyland, we do not need to excite everyone in every second.
“We were still in attacking mood (towards the end), so we have to prepare these moments better. We have a lot to improve, but it was a big step tonight as well."