Reds boss Klopp was furious that City captain Kompany escaped with only a yellow card from referee Anthony Taylor following his two-footed lunge on Salah in the first half at the Etihad Stadium.
Egypt forward Salah was able to play on after the foul, but Klopp insisted that was just luck because Kompany could have ended his season with the challenge.
The decision not to dismiss Kompany proved a crucial moment according to Klopp as City went on to snatch the points thanks to Leroy Sane’s late winner after Roberto Firmino had cancelled out Sergio Aguero’s opener.
“I really like Vincent Kompany but how on Earth is that not a red card? He is last man and he goes in,” Klopp said.
“If he hits Mo more he is out for the season.”
Unsurprisingly, Kompany disagreed with Klopp’s verdict and insisted he had made a firm but fair tackle.
“I thought it was a great challenge, was it not? I got the ball, a little bit of the man but it wasn’t naughty,” said Kompany, who was seen urging Salah to get up following the crunching tackle.
“I didn’t try to injure him. It was that or let him go through on goal.”
Klopp’s frustration at Kompany’s escape was exacerbated as Liverpool slumped to their first league defeat this season, ending a 20-match unbeaten run.
With the table-topping Reds hoping to win the English title for the first time since 1990, letting second placed City move back within four points of them was a significant blow.
Liverpool were rarely at their best and Klopp conceded the intensity of such a high-stakes game had affected his players.
“It was a big pressure. Very intense game. We were unlucky in our finishing moments. Unluckier than City I would say,” Klopp said.
“Sane scores and the situation with Sadio when he hit the post. They had periods where they dominated the game and everybody felt the intensity.
“Our expectations are high. We can play better. You have to take the game how it is. You can’t always dominate it.”
Klopp insisted Liverpool would bounce back from their first setback of what has been a dream season so far.
“I have already said to the boys this is OK. We lost it but it will happen. Tonight it is not nice but it is not the biggest problem,” he said.