Centre-back Kompany escaped with only a booking for a heavy first-half challenge on forward Mohamed Salah.
City won 2-1 as Leroy Sane’s 72nd-minute winner cut Liverpool’s lead at the top of the table to four points.
Klopp said: “I really like Vincent Kompany but how on earth is that not a red card?”
The German added: “He is last man and he goes in. If he hits Mo more he is out for the season.”
Kompany disagreed with Klopp’s assessment of his challenge, which came after an over-hit square ball from City team-mate John Stones while the game was still goalless.
“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,” the 32-year-old Belgium international said.
“I didn’t try to injure him. It was that or let him go through on goal.”
Klopp said that his team did not play at their best, but could consider themselves unlucky after Sadio Mane hit the post and Stones cleared off the line moments later in an early goalmouth scramble.
“Our expectations are high. We can play better. You have to take the game how it is. You can’t always dominate it,” he added.
“We were unlucky in our finishing moments. Unluckier than City I would say.”
The defeat was Liverpool’s first in the Premier League this season, ending hopes that they could repeat Arsenal’s 2004 feat of going a whole league season unbeaten.
But Klopp insisted that a four-point advantage over the defending champions with 17 games remaining was a strong position to be in as his side look to win a first league title since 1990.
“If somebody had told me after both games against Manchester City we would be four points up, I would have paid money,” he added.
“We want to finish the season as strongly as possible and we are still in a pretty good position.
“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.”