Rovers have defeated Bristol City and Derby County to reach the FA Cup fifth round and Appleton believes that his team are capable of advancing further in the competition.
Appleton told Sky Sports News: "It is a situation where we'll have a lot of fans travelling down to Arsenal on Saturday expecting the players to put in a right shift and give everything for the football club like they did on Tuesday.
"When you arrive at the stadium, you feel the buzz of the FA Cup, all of a sudden you genuinely believe that maybe this is another game that we can win.
"You just don't know, if Arsenal have an off day and we have a good day then you find yourself in the last eight and all your worries as to whether this is a game too much will be gone. We'd have a last-eight cup tie, maybe at Ewood Park against another big boy."
Blackburn are currently on a five-match unbeaten run under Appleton and sit in eighth place in the Championship.