The visitors showed little ambition to trouble the Reds, who dominated possession but could not create the chances in order to consistently ask questions of David de Gea in goal.
Emre Can and Philippe Coutinho's second-half efforts both demanded strong saves from the Spaniard, who helped preserve a hard-earned point on an underwhelming and frustrating evening under the floodlights.
But though United have been criticised for their defensive style, Klopp doesn't think their approach was out of respect for Liverpool's attacking talent.
Klopp: We had a few good moments, but nothing more
"I'm pretty sure the last thing Mourinho wanted to do was pay a compliment to my team," he said in his post-match press conference.
Klopp insisted that his opposite "thought about his line-up" and suggested it was "clear" that there would be "a lot of high balls in the game."
The effect of that meant that Liverpool, according to the manager, "needed to make pressure high" because of the threats of Chris Smalling, Daley Blind and Eric Bailly.
Klopp said that when United played "the long balls" it was "difficult" to deal with and continued: "Marouane Fellaini is immediately in our last row and Zlatan Ibrahimovic is there and Paul Pogba is there. It's really difficult to defend, but we did it really well."
He said that he didn't "watch the opponent too much" but that he could not "remember a lot of chances" and that he has "already had more problems a few times since we have been together in games like this" when the opposing team "is quite quick with long balls.
Klopp said that long balls weren't United's only approach, but that they were "one thing they wanted to do" as he hailed the Red Devils as a "very physically strong team."
"We had a few players who tried to make the advantage on the ground. Sometimes we were better, sometimes they were better," the German said, insisting it was "all okay" and that he wasn't "interested" in "why United were here."
He also accepted that while Liverpool "had a few good moments" they did not have "enough to deserve the win."
Maybe Lallana could have started, says Reds boss
The home side improved after the break, when Adam Lallana replaced Daniel Sturridge and Roberto Firmino moved into the frontman role, adding more energy and movement up top.
On what impact Lallana made off the bench, with the Reds' best spell of the game coming immediately after his introduction, Klopp said: "He's a good player, so it was no surprise."
The Reds boss explained that he "trained for two days" and that "maybe he could've started" because he was "really close" after a groin injury had forced him to withdraw from international duty over the recent break.
"Thank you to the medical department and the fitness coaches because they did a great job," he said on the Englishman's recovery, saying that he "could've played" after training but that "no-one knows for how long" he could have played.
But Klopp was pleased with the performance of the midfielder, insisting that he was "really sharp" and "greedy" to "feel the ball again" after he came on to the pitch.