Chelsea won their opening International Champions Cup clash 1-0 thanks to Gary Cahill’s header, but in a match of six bookings, Fabregas picked up a red for his 70th minute challenge on Estonia intentional Klavan.
Spaniard Fabregas after the match went into the Liverpool dressing room to apologise to Klavan and manager Jurgen Klopp.
“The way the ref was giving yellow cards, probably yes it was fair,” he said.
“In the Premier League, probably you could get away with it. I got there late, he got a toe to the ball and then I was anxious to win the ball. It was a hard tackle, so I accept it and move on.
“We want to win every game and everything becomes very competitive. But the ref for them and for us was giving cards all over the place.
“Sometimes when you do that as a ref you lose a little feeling of what is happening, because if you give one that is 50-50 or 40-60 then you have to give the next one. It became a bit of a farce. He didn’t have the game under control.
“It was the only little negative. I’m very happy with my performance, first game of the season. I feel very sharp.
“I feel great and feel the team is improving a lot, especially defensively.
“With the ball we have to improve a few more things but we should be happy.”