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The two sides played out a 0-0 draw at Anfield on Sunday and it means United remain top of the Premier League.
It wasn't the thrilling spectacle many expected, with Reds boss Klopp bemoaning the away side's lack of attacking threat.
He explained per BBC Sport: "The worst thing you can face in football is you play a side with world class players and they defend with all they have, deep in the box and good in counter attacking.
"So it's real difficult. That's the biggest challenge. But the way we understood the game, the way we felt the game, the way we reacted in the moments, that was really good.
"But it's not exactly like it should be so it means we will keep working on that. That's all."
Something tells us Jurgen Klopp wasn't too happy with the way Man Utd set up today... :grimacing:- BBC Sport (@BBCSport) January 17, 2021
Full interview :point_down: #bbcfootball
Liverpool didn't create many clear opportunities themselves and have now gone three league games without a goal.
It's the first time that's happened since 2005 and Klopp admitted his side now face a battle for the top four.
"I have to qualify for the Champions League and I know how difficult that is," he continued per The Guardian.
"This season will be a tough race for the top four that is for sure. Football fans are not the most patience species on this planet. They want to win each football game.
"I am not too different from that. But I am long enough in the business to know that there are more difficult periods.
"And this is not the most difficult period I have been through in my life, it's not even close. We have to be patient."
Despite Klopp bemoaning United's defensive approach, Solskjaer was 'disappointed' with just a point.
"No we didn't [do enough to win] because we didn't play well enough," the Norwegian told Sky Sports. "We grew into the game and towards the end you felt it's there to win, we created two big chances but two massive saves by the keeper.
"We can be more composed, some moments we missed when Marcus [Rashford] makes his run in behind, a couple of things we need to improve on.
"I'm a bit disappointed but you're playing a fantastic team and they had more possession. But the injuries they've had, you feel you [can] come here and get a result.
"We didn't, but a point might be ok if we win the next one. You want to win so you can't stand there smiling."
Featured Image Credit: BBC Sport & PA Images
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