The Dons face Falkirk in the third round of the League Cup on Wednesday and will be keen to make amends for disappointing displays in recent years.
But Shaughnessy warned that Aberdeen must treat this clash like a cup final or they may be denied one for real again this season.
The defender said: "We know it's a big game for the fans.
"With the disappointments we've had in recent years, it would be nice to have a cup run.
"The whole team believes that we can do something.
"It's just a case of going down there and performing.
"We need to treat it like a cup final or we might not get one."
Shaughnessy accepts that all the pressure will be on Aberdeen against the Scottish Championship side.
He said: "If you're playing a lower division side, you're always expected to win.
"We have no doubts it will be a hard game.
"There's pressure on us but there is pressure on Aberdeen going into every game, with the size of the club.
"So we know all about it."
Shaughnessy expects Falkirk to fancy their own chances when they host the Dons.
He said: "I'm sure they will go into the game full of confidence, with the results they have had and the way they have been playing.
"They are a young team and I'm sure they won't be scared of much.
"But we have to be full of confidence as well.
"We just have to go down there and play the way we know we can play and hopefully the result will follow."