Klopp charged down the Old Trafford touch line to berate Lovren late in his side's 2-1 defeat.
The German avoided being sent off by Craig Pawson, and Mourinho praised the referee for his decision.
"Probably you are not expecting my answer — I'm happy with the decision," Mourinho said during his post-match news conference.
"Because [Klopp] was not speaking against the referee. He was upset with a player and the same happened to me against Crystal Palace, where I was upset with my player and therefore they [the officials] understood that too.
"I think [fourth official] Martin Atkinson, after so many years of this, made the right decision. I saw it. [Klopp] was very upset with his player and not at the referee.
"If you leave the technical area by a couple of metres — or in this case, 20 metres — but to speak to your own player and not to complain about the referee's decision, they made the right decision."
Marcus Rashford scored a pair of first-half goals as United opened up a four-point lead in second on the table, while Liverpool fell to fourth.