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.
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.
Conte said: "I prefer not to answer questions about Costa - for me it's in the past".
The Chelsea manager told the BBC: "The sending off of Cahill was a key moment, because to play the rest of the game with 10 and then nine men is not easy".
Stoke started the second half in determined fashion but found good chances at a premium with Darren Fletcher coming closest when he seized on a loose ball 25 yards out and drilled narrowly wide from distance, and they were denied at the end when new home keeper Jordan Pickford made a fine stop from Xherdan Shaqiri.
Marcos Alonso had an effort saved by Burnley keeper Tom Heaton early in the second half before Alvaro Morata was brought on for Michy Batshuayi, and Alonso had a free kick saved soon afterwards. "After the red card we lost our heads, conceded two goals and then it's very hard to change the final result".
With the Blues and Liverpool returning to European football, and all top six clubs strengthening considerably in the transfer market along with Everton, Cahill believes the title race will be more open than ever. "We're going to work extra hard, even harder than a year ago, to make sure we compete". I am ready to fight with these players.
The defender has been handed the captaincy at the Premier League champions for the 2017/18 season following John Terry's departure.
Burnley won only once on their travels last season in the league, having to wait until their 18th away match to achieve it, and Sean Dyche admitted they had enjoyed some fortune in prevailing.
"Big decisions changed the outcome, quite obviously".
Vokes made it 3-0 at the break, and Conte was fuming. Here, these should keep you going until Match of the Day.
"Winning away from home on the first days quietens down some stories - we're written off at the start of every season".
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