Fabregas was sent off in the 81st minute at Stamford Bridge on Saturday with Burnley 3-1 up.
Gary Cahill had already seen red for a lunge in the first half but Alvaro Morata had got one back for Chelsea.
David Luiz scored after Fabregas’ dismissal but Burnley held on to record a famous victory over the nine-man Blues.
And according to The Times, Chelsea boss Conte is angry with Fabregas’ indiscipline having warned his players to keep their heads at half time.
They were 3-0 down at that point and already down to 10 men after Cahill’s reckless challenge on Steven Defour.
Fabregas picked up his marching orders with a second yellow card for lunging at Jack Cork having earlier been booked for sarcastically applauding a decision by referee Craig Pawson.
Conte has taken a dim view of Fabregas’ actions after his side’s opening day loss but also because it leaves him facing a midfield crisis ahead of Chelsea’s visit to Tottenham.
Spurs host Chelsea at Wembley on Sunday (4pm) after kicking off their Premier League campaign with a comfortable 2-0 win at Newcastle.
Conte is short in midfield following the permanent summer exits of Nemanja Matic and Nathaniel Chalobah to Manchester United and Watford respectively, while Ruben Loftus-Cheek is on loan at Crystal Palace.
Tiemoue Bakayoko has come in for around £40million but he is sidelined with a knee injury, meaning Conte has no other specialist central midfield players to start alongside N’Golo Kante against their rivals.
Chelsea defender Cesar Azpilicueta hinted at divisons in the dressing room after the game in a thinly-veiled dig at Conte’s signings.
“When you see the players we lost, and the players we signed in, they're not the same,” he said.
“We have good young players but we must know the reality that being champions is even harder the next season.
“We have experience of that so we need players - also for the development of the young players.
“They need help from top players, not to rush them in where maybe they are not ready to go at the moment.
“So it is something that the club are working on with the manager, and, hopefully, we can get new signings in the next few weeks.”
Source: Daily Express