Appleton was able to breathe in the sweet smell of success for the first time since taking over at Ewood Park, but he believes it should not deflect away from the fact that he still has plenty of work to do to turn their fortunes around.
Colin Kazim-Richards gave Rovers a first-half lead, with a superb goal from Scott Dann and a cool finish from Jordan Rhodes sealing their place in the last-16 as the second period wore on.
"I'm delighted to be making progress in the competition but I still believe we need to bring in a couple more players before next Thursday's deadline if possible," Appleton said.
"There is still plenty to play for in the league and areas where I would like to see us being able to call on reinforcements.
"I don't have a budget as such but I am sure the owners would support me if I went to them with a viable deal for the right players.
"Victory is all-important in the cup but keeping a clean sheet at a place like Pride Park is also a big plus for us.
"I believe in trying to build a platform and a structure that makes it hard for the opposition to score or get behind us and there were very pleasing signs of that sort of shape developing."