Winger Albert Adomah insists Bristol City can still beat the drop, despite a battering at Turf Moor.
It left Sean O’Driscoll’s Robins bottom and eight points from safety after just one win in seven.
But Adomah said: “It’s not over yet.
“We can still win all five games and stay in the league.
“We could even win four games and hope that other results go for us.
“We’re still in it, we’re just trying to survive.
City’s survival hopes would look brighter if they had held on to their half-time lead, secured by Adomah.
But Burnley skipper Jason Shackell nodded home on 52 minutes, before Chris McCann put the Clarets ahead five minutes later.
City’s Steve Davies then saw his late penalty expertly saved by Lee Grant and in stoppage time, Martin Paterson netted to wrap up the points for the home side.