Chelsea had an inauspicious start to the season when they lost Cahill to a straight red card within the first 15 minutes and Sam Vokes opened the scoring for Burnley at Stamford Bridge midway through the first half.
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.
Nevertheless, David Luiz pulled back a second for Chelsea when Morata flicked on a long pass from Azpilicueta, and the Brazilian was on hand to fire past Heaton for his second goal for Chelsea since rejoining the club last season.
Vokes' second goal came just before the half as he found himself unmarked in the centre of the goal and flashed a header beyond the despairing Courtois.
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He brushed aside questions about reported tension with Chelsea's board over signing new players and said he was not anxious because three key players - Eden Hazard, Pedro and Victor Moses - could return from injury and suspension for Chelsea's next game against London rivals Tottenham Hotspur at Wembley. "I don't want to comment on the referee, absolutely not".
"We have to improve a lot on this because after the first red for Cahill we lost our composure and conceded three".
While Antonio Conte has added to his squad this summer with the major signings of Alvaro Morata, Tiemoue Bakayoko and Antonio Rudiger, they've also continued to let players leave the club. In the next game I'm not sure whether Pedro is ready but for sure we'll have (the other) two players.
"We would have had defensive areas we need to work on if we'd won 3-2".
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In terms of teamnews, Sean Dyche has opted to go with a 4-5-1 formation, clearly created to frustrate the Blues.
"Today big decisions changed the outcome, quite obviously", the Burnley manager said.
"It quietens down a few stories", Dyche said to Sky Sports. "The first half pleased me because although Chelsea went to 10 men it was not easy".
Then it was a case of terrible defending that saw the visitors race into a 3-0 lead. And it was weird at half time because you have to decide how you're going to approach it from there.
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