Rovers return to league action at Hull City on Tuesday evening, three days on from their sensational fifth-round win over Arsenal at the Emirates Stadium.
Appleton's third game at the helm came in the previous round at Derby and a 3-0 success was his maiden triumph.
Blackburn took seven points from their three subsequent league matches and lie six points off the top six ahead of tackling the high-flying Tigers.
"If you're winning games of football you don't particularly feel as tired as you would do if you were losing games," Appleton said.
"I think it becomes a mindset. You've only got to look at Reading last year and the run they had.
"Going into the Derby game in the fourth round it was only my third game in charge and we'd just conceded a goal in the 98th minute (to draw 1-1) against Brighton at home.
"We knew it could be a big result for us and we wanted to win the game and since then we've gone on a great run so, in a way, the FA Cup has helped us.
"It was almost a catalyst for everything that's been good about the side over the last four weeks."