Danny Shittu's 43rd minute headed goal was enough to send the south London side through to a Wembley semi-final against Wigan Athletic as Rovers disappointed at Ewood Park.
"It is very disappointing as you could probably imagine the players are devastated in the dressing room," Appleton told Radio Rovers after the game.
"The lads gave me everything, they worked their socks off. We huffed, we puffed, we had a couple of chances in the second half, a goal-line clearance, but it just wasn't to be."
The manager didn't want to be drawn on whether the corner from which Danny Shittu scored the only goal of the game should have been awarded, more concerned with the way his side defended.
"I think it is debatable but ultimately whether it is given or not, you've got to make sure that you deal with it and you can argue about it later," added the manager.
"I think it is disappointing the way we conceded the goal. To lose out on a set play in that manner was disappointing.
"Wembley was the prize at the end of the game today, we knew what it was success or failure.
"We've failed on this attempt but there are ten games left this season, plenty of football and hopefully we can finish on a little bit of a high.
"There's no point grumbling about it. It is devastating for the players and everyone concerned, we just have to move on quickly."