The Red Devils secured a 2-1 victory over the Reds at Old Trafford on Monday night.
Despite that being the case, Klopp believes his team caused Erik ten Hag's side "massive problems".
As quoted by Anfield Watch on Twitter, he told ViaPlay the following: "We caused them massive problems. We were unlucky in certain situations, especially around the set-piece that we didn't score. That could have turned the game, hypothetical of course.
"But we had a good second part of the first half, so we wanted to build on that and showed the boys (at half-time) a couple of situations where we played exactly in the spaces where United couldn't even get (near) to us.
"I think there were really confusing defensive situations where nobody of them (United's defenders) knew anymore really where (Liverpool's attackers) were, but there were enough legs there so they could defend it. And we couldn't score."
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Anfield Watch Verdict
We don't entirely agree with Klopp's take. Yes, there were times when Liverpool threatened to score.
But, for the most part, the Reds were lacklustre in front of goal for the majority of the night. Manchester United were by far the better side, which is not easy to admit.
However, you do have to give the opposition some credit if they do play well. The Red Devils hunted Liverpool all night.
The two sides will meet again on the 4th of March at Anfield. Hopefully Liverpool can get some revenge against one of their biggest rivals when that particular day comes along.