The result has left them just three points clear of the bottom three, with three games remaining this season.
The Clarets manager said via the team's Twitter feed: "They were better than us. It wasn't good enough and they were by far the better side.
"That's Charlie [Austin]'s season over now and we need to do better. It's an opportunity for others.
"We're looking over our shoulders. We should be looking up but we have to dig deep now and be ready for the battle."
Burnley face newly-promoted Cardiff City on Saturday.