The first Premier League clash of the season between the two fierce rivals failed to live up to the pre-game hype, as Jose Mourinho's side kept the host frustrated for long periods at Anfield.
Zlatan Ibrahimovic headed wide with the goal at his mercy and David de Gea produced a sublime save to deny Philippe Coutinho, but chances were few and far between for either side, though Liverpool dominated possession.
Klopp was happy with a first clean sheet of the season outside of the EFL Cup, but was disappointed that his side could not break down United's stubborn rearguard.
"Mixed emotions," he told Sky Sports when asked for his views. "We didn't play as well as we could have done - that's the first thing.
"We started okay and immediately with their defending we weren't brave anymore, we didn't wait for the right pass.
"We created one-on-one situations, but they were maybe a bit better than we are with physical strength.
"They didn't have too many chances, maybe one where it was offside and then the header of Ibrahimovic. We had three or four, there was a great save from De Gea. It's a first clean sheet [for Liverpool], so yippee!
"We weren't calm enough - when you defend like Man United, that's their style, it's okay, you need to have respect but you need to be cool.
"It was a crazy game, that's not the way we want to play but now, more and more and minute by minute, I accept we got a point against Manchester United. There are worse things in the world."