Sean Dyche's side made life hard for Arsene Wenger's men and had some good chances to steal the game from Arsenal.
Burnley boss Sean Dyche took aim at referee Craig Pawson after a controversial Laurent Koscielny victor handed Arsenal a 1-0 victory on Sunday.
The Gunners snatched a late victor at Turf Moor as Laurent Koscielny netted a controversial goal to seal three points for the visitors.
Wenger insists that he did not see the incident that led to his side's dramatic victor in Lancashire, but was quick to hail the importance of the victory which lifts his side right into title contention at this early stage. "Our technique as well, we made some technical mistakes".
With seconds of the game remaining, a corner bounced off defender Laurent Koscielny - with Burnley appealing that the ball had hit his hand - and went in at the far post after Theo Walcott and Alex Oxlade-Chamberlain had got touches.
"That would have been the negative aspect of our game today had we not won".
Koscielny's victor gave Wenger a day to remember after his 20th anniversary at Arsenal, but the Frenchman admitted they had ridden their luck somewhat.
"We wanted to finish before the global break with a win".
Alex Oxlade-Chamberlain appeared to knock the ball on to the France global, with the ball eventually finding its way past goalkeeper Tom Heaton via Koscielny's arm.
In a rare Burnley attack just past the hour mark Petr Cech clawed Johann Berg Gudmundsson's header away for a corner before Chile worldwide Sanchez slammed a volley on to the outside of a post for Arsenal.
"The longer the game goes on and kept it 0-0 it makes it tougher and tougher for us - you know the outcome needs to be a goal soon and you start play a bit differently".
"Our analyst has it at six seconds over time, which is a lot", he said.
"If you add in the referee's part on the time and the handball, it is very frustrating".
"But that doesn't mean we're a side that doesn't want to take on the challenge because I think you saw that in abundance".