Saturday's defeat meant Chelsea have lost in their first opening game of the season since the 3-2 defeat suffered to Coventry in 1998.
Diego Costa is apparently going to play no part in the Blues' push to defend the league title this season - he is said to have been exiled by Conte via text - and was this past week spotted in Brazil playing a game of footy with his mates.
Chelsea's 2 players were also red carded in this match.
A red card for the captain, Gary Cahill, on 13 minutes was followed by goals from Sam Vokes, Steven Ward and Vokes again as Burnley produced a performance as controlled and purposeful as Chelsea were flaccid.
"Go four at the back, three in midfield, two up front and have a go".
Chelsea had their first real chance at goal 11 minutes in when Cesar Azpilicueta's low cross was deflected and almost sat up for Willian to fire home in the centre of the goal.
Stephen Ward compounded Chelsea's misery just after the half-hour mark when he controlled a long pass and beat Antonio Rudiger to lash home from a tight angle on the left. I'm very proud for this but today I saw two faces: "one positive in the second half and one negative in the first half".
The Blues forced goalkeeper Tom Heaton into a couple of smart saves, in a hope of regaining a foothold in the match.
Alvaro Morata, on as a second-half substitute, reduced the deficit in his first league start since a club-record move from Real Madrid for 58 million pounds ($75 million).
Morata thought he had his second when he bundled the ball over the line from Christensen's cross, only to see the linesman had flagged for offside.
But the recovery, if that what is was was short-lived as Fabregas was shown his second yellow card for a challenge on Cork on 82 minutes to reduce the champions to nine men.
With the clock winding down, David Luiz connected with a flick from Morata and pounded the ball into the goal for Chelsea's second of the game.
Conte returned to his mantra from last season that the team needed to work hard to produce results and he pointed out that Chelsea had finished their last three games without all 11 of their players on the pitch.