Colin Kazim-Richards scored the only goal of the game as Rovers knocked out one of the tournament favourites, the first time the Gunners have ever lost an FA Cup tie at the Emirates.
Speaking to Rovers Player
after the game, the Rovers boss said: "We are one step away from Wembley which is great for everyone at the football club and the fans.
"The supporters were magnificent, they really got behind the boys.
"I think it was important that in the first half we were defending that side where our fans were, because we knew that we had to stay in the game.
"We knew we had to get into hard time and to try to limit Arsenal to as few opportunities as possible and we did that. So I was glad that our fans were on that side, and on our side throughout, they were tremendous."
Rovers' name is in the hat for the 6th round draw later this Sunday, with Appleton having no preference as to who they could face, particularly after overcoming Arsenal on their own patch.
"I don't think it is about fearing anyone, there are some great teams left in the competition," added Appleton.
"Let's get the draw, let's see who we can get and we'll take it from there.
"We are only one game away from Wembley, it is a great opportunities for the lads, it is only 90 minutes and whoever it is against we'll be giving it our best shot."