The highly-anticipated clash saw City narrow the gap at the top of the Premier League table to just four points after goals from Sergio Aguero and Leroy Sane cancelled out Roberto Firmino's second-half strike.
The match started at a frantic pace and City captain Kompany received a yellow card from referee Anthony Taylor just after the half-hour mark after a lunge on Salah.
The Belgian centre-back could easily have been given his marching orders after Salah was left in pain on the deck.
Speaking after the game, Kompany said: "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. I didn't try to injure him. It was that or let him go through on goal."
However, Klopp believes that it was a certain red card for endangering his player, whilst he summarised his thoughts on an "unlucky" night for the Reds.
"It was a big pressure. Very intense game. We were unlucky in our finishing moments. Unluckier than City I would say. Sane scores and the situation with Sadio when he hit the post," he said.
"They had periods where they dominated the game and everybody felt the intensity. But we came back and had big chances. It is always like this. You have to score in those moments. When Aguero scores there is no angle. In similar situations we didn't score.
"It was not our or City's best game because we both made it difficult for the other team. 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.
"I really like Vincent Kompany but how on Earth is that not a red card? He is last man and he goes in. If he hits Mo [Salah] more he is out for the season. It is not easy for the ref and he may not see it how I see it.
"Our expectations are high. We can play better. On the other side it was an intense game. You have to take the game how it is. You can't always dominate it.
"With a bit more luck we could have got 2-2, which would be perfect for us."
Kompany, speaking to Sky Sports after the game, went on to heap praise on his teammates, whilst conceding the title race is still in Liverpool's hands.
"I'm not worried about the result I'm buzzing with the tremendous performance. We went toe to toe with a very aggressive team and we matched them," he added.
"It's still in Liverpool's hands. It came from our guts, a desire you can't describe. We are a better team when we play with emotions."