Rovers found the going somewhat harder than they have done in recent weeks. They were excellent in a 2-2 draw against Nottingham Forest and then won 1-0 at Sheffield Wednesday, with on-loan striker Federico Macheda scoring all three goals.
The Italian had their best two chances in this one, hitting at goalkeeper Tom Heaton and then wildly over, but their downfall was mistakes at the back.
Richie Wellens was dispossessed cheaply which led to Rob Jones hacking Sam Vokes down and the Clarets striker converting the resulting penalty, before the centre-half bundled into his own goal as Kieran Trippier ripped in a late cross.
"We're disappointed to get beaten and a little bit frustrated, especially with the goal on half-time. We had two or three chances to clear the ball," manager Dickov said of the build-up to Vokes' spot-kick.
"When you get beaten by the better team you have to hold your hands up and not make excuses and that's what happened.
"You have to give Burnley credit. They're a good team, they're top of the league for a reason. I would rather concede a goal late on when we're pushing to score than in another way.
"Burnley did the basic things in football and that was the reason they won the game."