Rovers bowed out of the cup with a whimper on Wednesday night when they lost a quarter-final replay at home to Millwall, their seventh game without a win.
Blackburn failed to score in six of those matches but Appleton believes that a victory at Ewood Park on Sunday will get their season back on track.
"It's an opportunity to put things right very, very quickly," said Blackburn manager Appleton.
"A victory against Burnley on Sunday will go a long way to making me feel better than I do at this present moment. I'm sure it will be the same for all the fans."
Blackburn have 10 games remaining and Appleton says they need to win at least three games to avoid back-to-back relegations.
"It's a situation where we've just got to make sure that we take care of the next game and the next game's a big one against our local rivals," he said.
"I think three points against Burnley on Sunday will go a long way towards what will hopefully be a positive end to the season.
"I'm not worried about a hangover (from the Millwall loss) because, within 10 seconds of the kick-off on Sunday, the fans will make sure the players are aware of how important the game is."
Should Burnley emerge victorious at Ewood Park it will be their first victory against their east Lancashire rivals in 10 attempts stretching back to 1979.
"Any game's a good game to bounce back but never more so than if you're playing the club down the road who everyone wants to beat," said Clarets boss Sean Dyche.
"At the moment you're going into that with freedom because everything's on their side - 34 years, nine games, our team not firing as clearly as we'd like.
"So that's a challenge but possibly that brings us freedom just to go and play, go and get on with it, because eventually we'll get those clear minds."