Rovers became the first side to beat Arsene Wenger's men in the competition at the Emirates courtesy of their shock 1-0 win on Saturday.
"I think if you look back on recent stats, not just Blackburn versus Arsenal, Arsenal against any team at any level at the Emirates in cup competitions and we could stay here for ages and talk about how many times they've turned over teams by five or six goals in recent season," said Appleton.
"They'd never lost an FA Cup tie at the Emirates. I can't remember the last time Blackburn kept a clean sheet away to Arsenal.
"So if you put all the facts and stats together it's one hell of an achievement. I said to the players after the game, 'don't play down what an achievement, what a performance and a result this has been today because it's as good as you'll ever get in your career'.
"But, having said that, I did ask them very quickly to make sure that we move on and make sure that we fully concentrate on what's going to be a tough game against Hull."
Second-placed Hull City host Rovers on Tuesday, with Appleton's side looking to continue their recent good run to try and close the six-point gap between themselves and the play-off places.
"Since I walked into the football club I've tried to improve the mentality of the players on a day-to-day basis and going into the games, making sure we're harder to beat and respecting the division because we've got a few players who've played at a higher level for quite some time," added Appleton, who has overseen four wins from seven games since taking over as Blackburn manager.
"I also want to make sure there's normality about the football club and everyone not associated with the football club is talking about football because, ultimately, that's what we get paid to do.
"The results count for a lot of things, but if the players know that when they come into the football club they're going to go into an environment where it's stable and it's nice to work at, then they're going to produce their best football.
"I have a points target myself but it's not a discussion that I've had with the players. I want the players to be focusing on the mentality of trying to win every game."