In 2008 Harry Redknapp's Pompey went to Old Trafford in the quarter-finals and stunned Manchester United 1-0 on their way to lifting the trophy. Administration and relegation have since taken their toll at Fratton Park, with Pompey now 17th in the npower Championship and yet again looking for new owners.
And Appleton admits a win at Stamford Bridge would be an even more impressive achievement than victory over United, saying: "It would be bigger than that, because a lot has happened to Portsmouth since then."
He added: "We're in the Championship now with a small squad and a lot of players who are coming towards the end of their careers.
"But we're in good form lately and hopefully we can be one of those teams around the country celebrating a shock this weekend.
"Chelsea haven't had a fantastic first half to the season, but they had a good win at Wolves earlier this week which will have lifted them, and this is a competition they want to win.
"We just have to hope they go into the game with the attitude that they're facing a side in the bottom half of the Championship, and that we then catch them off guard."