Rovers are now seven points behind sixth-placed Brighton in 10th position, a point and a position behind Leeds.
Appleton suffered a further injury blow after Colin Kazim-Richards limped off with an ankle problem early in the second half at Ewood Park.
The manager also revealed midfielder Dickson Etuhu is likely to miss the rest of the season after a recurrence of his medial knee ligament injury this week.
Meanwhile, full-back Martin Olsson will be out for around a month after a ball struck him in training on Friday and caused internal bleeding in his eye but Appleton is trying to remain positive.
"When I walked into the football club nobody had any thoughts whatsoever about getting into the play-offs," he said.
"I think a lot of the damage was done before I arrived but, saying that, there's 13 games to go.
"The message to the players after the game was you just need to keep knocking on the door.
"If you keep knocking on the door and asking questions hopefully someone will slip up, and generally someone does.
"There's still a lot of games to go and if we're still in and around it with six or seven games to go, that's the time to really start putting the pressure on."