Spain international Fabregas was dismissed in a feisty opening International Champions Cup exchange in California, when his studs up challenge felled Estonian Klavan.
In a game that saw six yellow cards as well as Fabregas’ red, Chelsea came out winners thanks to Gary Cahill’s tenth minute header.
But Klopp, who also saw midfielder Marko Grujic taken to hospital with concussion after a clash of heads with Bertrand Traore, revealed that after the match Fabregas had apologised to he and his player.
“Sometimes in life if you are too late then you get a red card. That’s how it was.
“The biggest problem for me is that Marko Grujic is in hospital. He can’t remember anything. That’s not too cool for a young boy in this situation.
“When a team with the quality of Chelsea defend so deep then any team in the world would have a problem.
We had more possession against a good side but we have to accept that we lost.”
“I am sorry for him and the Liverpool player. In this period it is easy to go too late into a tackle. I know Fabregas is a good man and a good boy and he is not the type of player to have this situation.
“When two great teams face each other nobody wants to lose, and for this reason we saw a competitive game. I am pleased because I saw the right spirit, I saw a lot of positive things. When we played with ten men we did not suffer despite having one man less. I saw a lot of positive things.”