The Red Devils, who played with a back five, only had 32 per cent possession during the match as they defended for long periods after Marcus Rashford gave them a first-half lead.
But Adam Lallana earned the away side a point with a strike five minutes from time to keep Liverpool's unbeaten start to the Premier League season alive.
When asked about their opponents' tactics, Klopp pointedly said United consistently sat deep in defence whenever his team came to the Theatre of Dreams.
"[Man Utd's style] doesn’t frustrate me," he said post-match. "I’m not the person who should be concerned about this style.
"It’s just a fact that when we come here, they just defend. It’s OK, no criticism, it’s just a fact.
"When United plays Liverpool, usually you’d think both teams would play like this, would try. We are the one team everyone is on their toes when United play us.
"With the quality they have, the way they set up is really difficult.
"It’s no excuse. I thought we could do better today. But you cannot play each team like this."
Four of the last five United-Liverpool games at Old Trafford have ended in draws, with the home side's 2-1 win in March 2018 the only outlier.
Klopp suggested United's defensive set-up on their own pitch was a product of Liverpool's current strength, but admitted his team didn't play well on the day.
"We don’t have to say it’s a compliment," Klopp said. "It’s just that we are a good team and it’s normal that people think how they can stop us.
"Today we had a big say in that – we stopped ourselves!
"But of course United defended really well and then had the speed with James and Rashford. They chip the ball in behind and then the race is on! That’s not cool.
"We defended OK, but we should have played much better football. That’s what we expect of ourselves.
"No criticism or judgement of United, it’s just about ourselves."