An underwhelming outing from both sides, Liverpool struggled throughout the contest to create many clearcut chances - despite recording a total of 34 shots at Andre Onana's goal.
A dominant yet unproductive outing, Klopp is frustrated that his side were unable to take all three points.
"The main thing I don't like is the result, we should have won the game," he told BBC Sport.
"With that number of finishes a few more should have been on target. It should have been more, but there were some things I liked. The counter pressing was the best with this group, the intensity and the start was probably our best so far.
"This today hurts, it is good, it gives us a lot of information as well and now we have to finish the situations off.
"Some situations were where we shot from distance when there was probably a player in a better position. It is okay, you need one goal and everything would be right."
Despite the infamous 7-0 only occurring last season, Klopp has singled out today's game as Liverpool's most dominant against Manchester United.
"I can't remember this kind of dominance against Manchester United as we did today," he added. "It was special, the atmosphere was special.
"We had moments where we looked like we were in a rush. We played a few long balls a bit too much.
"In possession, when we built with three, they had no solution. We should have maybe used underlaps and overlaps more but when you arrive the box is full.
"From a passion point of view Manchester United played a fantastic game, they put everything into it. When a team plays with this much passion you have to break the rhythm.
"The attitude today was top, top, top. I wish we would have won but we have a point more and that is okay."