With 20 minutes left in the bad tempered pre-season clash, the Blues midfielder caught Klavan late on the ankle.
The Spaniard was given a straight red card from referee Baldomero Toledo for his challenge but Chelsea held on for a 1-0 win.
After the match, Klopp refused to criticise Fabregas and confirmed Klavan had escaped serious injury.
“It’s a red card and I hope it’s not a mentality issue,” Klopp said.
“He (Fabregas) came in the dressing room and said sorry, he came too late in the challenge.
“Sometimes in life if you are too late then you get a red card. That’s how it was.
“It was just a knock for Klavan. I think he will be okay.”