The Reds were 20 games unbeaten in the league until their trip to the Etihad, and despite a valiant effort, they eventually lost 2-1 after Leroy Sane fired in a second-half victor for Pep Guardiola's side.
Referee Anthony Taylor gave Kompany a yellow card in the 31st minute for what Klopp deemed a reckless lunge.
He told Sky Sports: "I really like Vincent Kompany".
Premier League - Follow the Football match between Manchester City and Liverpool live with Eurosport. In their earlier matchup, they played to a 0-0 draw, with Riyad Mahrez missing a late penalty that would have swung the pendulum in Man City's favor.
City are not the force they were last season, by any means, and the style of last season's title success was replaced by a more direct, uncompromising approach against Liverpool. If Mo can go through, come on, what happens then?
"We want to finish the season as strongly as possible and we are still in a pretty good position".
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"I thought it was a great challenge, was it not?"
Liverpool can claim they were unlucky at the Etihad, then, because on another day Mane's shot would have gone in off the post and Sane's would have deflected out.
"It is the toughest situation I have to handle", Guardiola said at the time.
That man was injured full-back Benjamin Mendy who sprinted onto the field to embrace Sergio Aguero and was amazingly chased down by stewards who had mistaken him for a pitch invader. "But it was that or let him go through on goal and the decision was made very quickly in my head". "We can use that to our advantage and we'll look forward to the games ahead now".
However, Klopp insists he would have paid a insane amount of money for Liverpool's current position at this stage of the season.
"I would have paid money for it you can not believe", Klopp said.
"We ran a lot and fought a lot and everyone could see how much we wanted to win the game".
"We have not lost it". There were moments in the game where we had the momentum, but unfortunately we got done with the second goal.