United held Klopp's attractive side with relative comfort, thanks to the tactical excellence of his stifling set-up and a couple of blinding saves from David de Gea yet they offered precious little in attacking invention and creation.
Their two mega-signings of the close season, Paul Pogba and Zlatan Ibrahimovic, combined for their best moment, only for the Swede's close-range header from the Frenchman's cross to bumble harmlessly across goal.
This summed up United's blunt edge and left one of their distinguished old boys, former England fullback Gary Neville, watching from the Sky Sports studio, to opine: "I don't think this team are ready to win the league.
"They don't have the quality to counter-attack at pace."
Mourinho, though, was adamant: "We controlled the game not just tactically but the emotion of the game. That was probably the quietest Anfield I had and I was expecting it to be the other way. I think was a positive performance."
He reckoned the British media had been swooning about Liverpool's form and declared: "They are not the last wonder of the world like you like to say they are.
"People expected us to come here and be really in trouble, which we were not."
Yet United did not create much trouble for Klopp's side either and, still lying seventh in the league with plenty of enterprising quality above them, they will be expected to deliver something more convincing in their two other big dates this week.
They host Fenerbahce in the Europa League on Thursday before Mourinho has his fascinating return on Sunday to the Chelsea den where he was once worshipped.
Pedestrian performances there could raise fresh questions about a manager who is already looking at the lowest points total he has gleaned at any new club after his first eight league games since his early days as a novice boss in Portugal.
Klopp, having to settle for his part for only the second goalless draw between the sides in the Premier League annals, conceded that Mourinho had been a master of the defensive arts again.
"That kind of defence is difficult to play. The man-marking is really difficult, they are stronger than us.
"I am not frustrated but I am not happy with the performance. No-one will show this game in 10 or 20 years but we could have played better."
The German was left with questions of his own as Daniel Sturridge's disappointing performance must have made him wonder again where exactly the England striker fits into his high-pressing attack.
(Reporting by Ian Chadband; Editing by Clare Fallon)
