United produced a fine defensive display to secure a point against their old rivals.
David de Gea pulled off a number of good saves for the Red Devils, including a world class stop to keep out Joel Matip.
Liverpool were wasteful in front of goal and couldn’t find a way through United as Jose Mourinho’s defensive game plan worked yet again.
Klopp was annoyed with how United played, insisting such tactics would not be acceptable at Liverpool.
He said: “Manchester United came here for a point and got it. For sure you could not play this way at Liverpool but it's OK for Manchester United.
“[It was] a good performance, I thought worthy of three points. We were unlucky in at least two, maybe three situations - of course the big chance when De Gea made the save.
"There were a lot of good individual performances. Even when the last few games for us were not perfect, we were clear and concentrated.
“When an opponent has this kind of defensive approach you will not create 20 chances.
"I felt the referee should have given us a penalty. Then, maybe, it was a red card with the Lukaku and Lovren situation. Two situations, with different outcomes producing maybe a different result.
“We need to be creative and brave in a situation like we are in. We don’t score easy goals anymore so the biggest challenge is not to lose confidence and we haven’t.
“We carry on. I told the boys already they took the hard way when they decided to join Liverpool."
Liverpool defender Joe Gomez, the man of the match at Anfield, said: “It is a bit frustrating with the chances we had.
“We will take the positives of a clean sheet and point against good team
“They had a couple of chances but we are frustrated for not winning.”
And Matip added: “We had a lot of possession. We had more than them.
“It was a great save from David De Gea. I had to score and maybe we would have won. His reaction was brilliant.”
