Rovers produced an impressive 3-0 victory at Derby in their all-npower Championship fourth-round tie on Saturday and their reward is a last-16 showdown with Arsene Wenger's side.
"I don't think we could have been picked against tougher opponents," Appleton told Rovers' official website.
"It is obviously going to be a good cup tie, I expect we'll have plenty of support travelling down there. It is a great stadium with a fantastic pitch.
"The tie is a great opportunity for the players to pit their wits against the best and express themselves, but they don't come much harder in terms of away ties.
"It would have been nice to play them at Ewood Park but it is 11 v 11 at the end of the day, it'll be a day off from the league for us, we'll be able to go there with no fear."
One man who looks set to miss the Emirates Stadium encounter is Blackburn forward Josh King.
The former Manchester United youngster returned following three games on the sidelines to face Derby, only to suffer a recurrence of his hamstring injury in the opening stages.
"It is his hamstring again, it is the same problem," Appleton added. "He's done a million and one tests in terms of his strength and we thought he was right.
"He felt right, he felt great and wanted to play so it's a shame because we are going to miss his pace in his side. That is something we'll have to look at."