Jurgen Klopp's side dominated from start to finish but were forced to settle for a point as neither side could find the back of the net.
Sixty-two percent possession, 19 shots at goal and five on target just about sums up how dominant the Reds were.
Speaking after the game, Klopp hailed his "unlucky" players and said their performance deserved victory.
"I think the performance was worth three points, we were the better side," said the German. "I think Man United came here for the point and they got it. We wanted three points and didn't get it.
"It's quite difficult when a top-class team like Man United has that defensive approach. You're not going to get 20 chances. We were unlucky."
Only once was Liverpool's defence really tested throughout the 90 minutes, when Romelu Lukaku fluffed his lines after being put through one-on-one with Simon Mignolet.
Mignolet produced a fine save to deny his compatriot, who was unusually quiet and had to wait until the 17th minute for his first touch.
It's not often Liverpool look so resolute in defence - they've already conceded 12 goals this season - but against United, Dejan Lovren was particularly fantastic.
It's hard to pinpoint exactly what was different about Liverpool's back line, but their inconsistency is still a problem that needs solving.
Only Klopp can do that and he appeared to unintentionally reveal his defence's biggest issue in an interview with Jamie Carragher on Sky Sports on Friday.
In the video below, Carragher asks Klopp what Philippe Coutinho's best position is, to which Klopp responds by saying he "doesn't believe too much in positions". Check it out.
Klopp says: "I think he (Coutinho) can play both positions, and the third one, and the fourth one, that's how it is. I don't think it makes a lot of sense to know where is his best position.
"Having him on the pitch is a good thing to have. I don't believe too much in positions, it's about when we have a system and everyone knows where my first responsibility to defend.
"The rest should be fluent, should be flexible, should be different movements. If you then do it right, if you lose the ball, you have a short way back into a defensive formation."
Here potentially lies the problem with Liverpool's defence - and their squad in general. If Klopp isn't giving his players set positions, that could be why so many gaps appear at the back.
Individual mistakes have also played their part, of course, but that all stems from a lack of team cohesion.
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