The Spanish midfielder knew it was a bad tackle and visited the Liverpool dressing room after the match, according to Jurgen Klopp, to apologise to the Estonian defender.
Fabregas has now issued a public apology to the Liverpool new boy, who joined the Reds from Augsburg this summer, via Twitter.
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“Great team performance last night and important to get back to winning ways. I'm feeling very good and strong,” the 29-year-old tweeted to his 8.5 million followers.
“I’m very sorry for my late challenge on Ragnar Klavan. There was no malicious intent and very relieved that he is ok.”
Liverpool fans react
Here’s how Liverpool fans reacted to Fabregas’ tweet…
Chelsea fans react
And now some reaction from the Chelsea supporters…
Fabregas assisted Cahill's goal
It was Fabregas who provided the assist for the only goal of the game; his corner was met by the head of Gary Cahill, who rose highest to nod past Liverpool’s new goalkeeper Loris Karius.
Although these matches are mainly played to boost fitness levels, Antonio Conte will no doubt be very happy that his side managed to record victory over a team expected to compete for a top-four finish in this season’s Premier League campaign.
Conte blames tackle on fatigue
Conte put Fabregas’ tackle down to tiredness rather than malice in his interview after the match.
"I think that the fatigue sometimes can bring a player to go too late," the Italian coach was quoted as saying by BBC Sport.
"I know Fabregas is a good man, a good boy and is not a player to have this type of situation. I'm sorry for him, I'm sorry for the Liverpool player."
Next up for Chelsea is a tough match against Real Madrid on Saturday night. The Blues then take on AC Milan and Werder Bremen before their Premier League opener against West Ham on August 15.
Did Cesc Fabregas deserve a red card for his tackle? Have your say by leaving a comment below.