Having seen two old adversaries cancel each other out on Merseyside, Klopp was quick to question the approach of the visitors.
He told Sky Sports on a United side that he believes offered little attacking intent: "For sure you could not play this way at Liverpool, but it's OK for Manchester United.”
Mourinho wasted no time in biting back at his coaching rival, with the Portuguese insisting that he played to win and that containing tactics from the hosts contributed to an uninspiring contest.
He told Sky Sports: “We came for three.
“In the second half, we felt it was difficult to do that with the match dynamics.
“I was waiting for Jurgen to change for him to go more attacking, but he kept the three strongest players on in positions where they were having control. He kept the strong midfield and that midfield was stronger than mine.
“You’ll say we were defensive and they were offensive. They were at home and didn’t move anything.
“He did well and didn’t let the game break. [Emre] Can and [Georginio] Wijnaldum were very good from a defensive point of view.”
Chances were few and far between in a heavyweight encounter between two Premier League title hopefuls.
David de Gea did repel one effort from Joel Matip during a keenly-fought first half, with the Spaniard once again highlighting his value to the United cause.
Romelu Lukaku came as close as anybody to breaking the deadlock for the Red Devils, but the £75 million striker failed to beat Simon Mignolet when presented with a clear sight of goal.
The game then fizzled out after the break, with neither side mustering a shot on target in the second 45.
A draw was enough to send United to the Premier League summit, for a few hours at least, while stretching Klopp’s impressive record in meetings with fellow ‘big six’ sides.