Conte made a tactical reshuffle after Cahill's exit, Andreas Christensen coming on for Jeremie Boga, who had been named a surprise debutant due to Pedro's injury.
Chelsea were starting to force the issue after a slow start, but the champions were reduced to 10 men in the 14th minute when captain Cahill was handed a straight red card for a late challenge on Steven Defour.
Nicholas says Conte may not have actually wanted to come back to Chelsea after his summer break but now must show he is fully committed.
Burnley reinforced the point, ruthlessly ripping apart the home side at Stamford Bridge.
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It was really an terrible day for Chelsea who ended the game with nine players.
"In recent games we have finished with nine or 10 men". I thought the referee was very good - he had a tough game to handle. " Despite a great result, the manager still recognised some errors, citing "two soft goals we gave away" but nevertheless "a very good win is pleasing" for him".
"You don't know me very well", Conte said, replying to the suggestion he might have meant to highlight the club's lukewarm summer recruitment. "Instead we conceded three goals and despite a good second half performance it was hard to change the result". It is not a secret that Antonio Conte wants his club to sign a few more players before the end of the transfer window as Chelsea have so far signed Caballero, Rudiger, Bakayoko and Morata.
"As for the transfer market, the club is trying to do the best".
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Still, he said the United States is edging closer to war with Kim because of his nuclear provocations. "But we are closer to war than we were a decade ago".
"That's why I think it's harsh, but I've had many replays to see it looks harsh".
Chelsea down to 9 men. But, do they form a great partnership?
After beating Tottenham to the Premier League title last season, the Blues can expect a fired up performance from their London rivals in their temporary Wembley home next Sunday.
"Big decisions changed the outcome, quite obviously. I have to try to adapt a new system and to anticipate this situation of playing with nine or 10 men in the next game".
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Stamford Bridge then fell silent in the 43rd minute after Sam Vokes got his second to make it 3-0 and give Antonio Conte's side a mountain to climb. And it was weird at half time because you have to decide how you're going to approach it from there.