Rovers go head-to-head against the fellow npower Championship side, the prize, a semi-final place at Wembley.
The Rovers boss believes that Sunday's match at the Den will give both sides the chance to put aside the pressures of the league campaign and enjoy the occasion of a last eight tie.
"I think this is an opportunity to put the league to bed for a few days," said Appleton.
"We've got a great opportunity to go and play at Wembley, it has been a while since the football club did that.
"So I'm sure the players will grasp that, they've got an opportunity to do something special."
The Rovers boss sees the match against Millwall as a chance to give the club a boost going into the last ten matches of the season after a disappointing few weeks results wise.
"It has been a poor couple of weeks for us," added the manager.
"We have had a lot of games but they haven't gone our way for one reason or another.
"So there are so many good things that could come out of the game on Sunday. At least we've got an opportunity to be part of that.
"There is no shying away from it, I'm sure Kenny Jackett will be thinking the same thing.
"it is a quarter-final cup tie, two Championship teams going head-to-head knowing that the likelihood is that the winners will play one of the big boys at a magnificent stadium.
"It is all to play for, it is going to be tough to call. Millwall will go into the game as favourites being the home team as well as us having a host of players cup-tied and out.
"You just don't know, maybe it is someone's opportunity on Sunday to be a hero."
Tickets for Sunday's cup tie will be on sale at Ewood Park until Friday lunchtime. A limited number will be available on the day of the game at the North Stand ticket office from 12 noon.
Prices are £20 for Adults, £11 Seniors aged 60 and over, £10 for Juniors under 16. Call the ticket office on 0871 222 1444 for further information.