The Reds couldn't break down Jose Mourinho's visitors at Anfield with David de Gea saving excellently from both Emre Can and Philippe Coutinho in the second period to keep the score goalless.
And they had to settle for just a point as they ultimately failed to penetrate United's organised and resolute back-line, though it was a point that puts them just two off table-topping Manchester City.
German boss bemoans Reds' lack of patience
Klopp completely dismissed the idea that his side were affected by the tag of favourites going into the crunch clash, insisting that it wasn't "that important" because they are "quite often the favourites" and are "used to being the favourites."
"You could see in this game that Man United are physically a little bit stronger than we are," he admitted in his post-match press conference, before declaring that it was obvious to everyone that they could "have played better."
The manager bemoaned that his side "couldn't get rid of the hectic [pattern of play]" which was "the problem", saying that they needed to "calm down immediately" when in possession.
Klopp insisted that is what Liverpool "didn't do" and so they "wasted a lot of energy in the first-half" because they "made so many runs that were not necessary" after the "wrong pass."
He explained that his team "had to run a lot because of our bad passes" and added: "In the second-half, with fresher legs, we could've caused them more problems."
Klopp suggested that this wasn't a "reason for being frustrated or something" but only "the information [to take] from this game", insisting that it was at least "better" that they got one point when last year they lost, but that they can still "do much better."
Further explaining the nature of the game, the Reds boss continued: "The game was, from the first second, very hectic and that was maybe what United wanted and what we didn't want. It was more to their advantage than us."
He said that "that can happen at the start" because they "don't always have an influence on the start", but Klopp insisted that they still "have to find a way back to the way you usually want to play."
He was therefore disappointed with his side in that they "lost patience much too early" - which he called only "the first problem" - and then their "passing game was not good anymore" as a result.
Klopp also felt that Liverpool "have to do better things" with the ball given that they had "65 per-cent possession", adding: "In the first-half we could have had, with two better passes, two 100 per-cent chances, which we didn't."
My players can, and need, to do "much better" - Klopp
He praised De Gea for his "brilliant saves" in the second-half and admitted that Zlatan Ibrahimovic had a header which "would usually finish."
"The second half, maybe we would have deserved the win but in the end, the best news tonight is we have one point more and a clean sheet," continued Klopp.
He added that they "can do much better" and "have to do much better", vowing that they "have to learn in a game like this" to "stay cool" when an opponent "creates an atmosphere on the pitch like this."
The Reds boss said that United "wanted to chase us in one-on-one situations", insisting his players needed "calmer movements" so that they needed less distance "to make an advantage" but said that they "immediately lost patience" once in "the first and second thirds of the pitch."
He explained: "It was like 'now give it [the ball] to Daniel Sturridge' and of course, it was a really difficult game for a striker. The way we played today, it was not easy to enjoy for a striker."
Klopp bemoaned one particular moment in the first-half when Coutinho "made a brilliant run" and "wanted to pass to Daniel in the box" when he should have found the "completely free" James Milner, who "could have made a cross from the touchline with three or four players in the box."
He also said that "situations like this" are why they "could have done better" but still said that "there was a really, really good attitude" from Liverpool who "worked really hard and tried everything" but "with the wrong tools."