The Italian's greatly depleted team became just the second defending Premier League champions to lose their first game of the season, as they suffered a first-half collapse to go 3-0 down after Cahill had been sent off in the 14th minute for a reckless lunge, with Cesc Fabregas later receiving a second yellow card too.
Former England captain Alan Shearer had said of Chelsea that there is "something brewing which isn't nice" and their first-half implosion in a thrilling match would appear to give his view credibility.
Alvaro Morata nearly inspired a comeback as a second-half substitute, scoring before setting up a late strike for David Luiz, a goal that came after Cesc Fabregas' removal for a second yellow had seen Chelsea reduced to nine men. And we responded very well.
Conte has grown frustrated with the lack of progress the Chelsea board have made securing some of his top targets this summer and is hoping that three more signings can be made by 31st August.
"In the second half it was very hard to change the final result, despite the great commitment, the great desire, the great will of my players". "But for sure he played very well in the last 30 minutes, which is good news for us".
"I thought we were strong early in the game, while it was 11 v 11".
In just 13 minutes, Chelsea skipped Gary Cahill was seeing red after a late tackle, allowing Burnley's Sam Vokes to quickly hit the net twice before half-time, whilst Stephen Ward also opened his account for the season.
That was due in part to the belief that Burnley now possess, having retained their Premier League status last season.
"Your first win of course is always important when you are written off like we are every year".
"It quietens down a few stories", Dyche said to Sky Sports.
Chelsea have once again loaned out a string of young talent this season, and have sold the likes of Nathaniel Chalobah, Nemanja Matić and Nathan Aké to Premier League rivals.
"But we're not getting carried away, it's a great result, brilliant for our players and supporters, but we know there's a big season ahead of us, and everyone is telling us it's a big challenge".
"It was a key moment because after that red card we conceded three goals, but we must pay attention because there is the whole rest of the game to do your best", the manager said.