Saturday's eagerly anticipated encounter was not as bad as last October's meeting on Merseyside, but this was another edgy, scoreless 90 minutes.
Klopp's men bossed the possession and the shot count at Anfield, where he felt United played in a way that would not be accepted by Liverpool fans.
"I think the performance was worth three points," the Reds boss told Sky Sports. "We were the better side.
"I think Man United came here for the point and they got it. We wanted three points and didn't get it.
"I'm sure if we played like this, you could not do this at Liverpool. Obviously for Man United it is OK.
"It's quite difficult when a top-class team like Man United has that defensive approach. You're not going to get 20 chances.
"But we had enough – a big one in the first half, and a penalty I feel. We were unlucky."
Klopp, seemingly having cooled off, tiptoed around the matter in the post-match press conference when asked whether he would line up a side like Mourinho did.
"Nice question," he said, with a smile. "If I say no, 'you don't want to win something'. If I say yes, then people are already afraid, so no comment."