Rovers take on Millwall at the Den on Sunday afternoon in a quarter-final tie which guarantees there will be a side from outside the Premier League elite in the last four.
The Ewood Park outfit booked their place in the latter stages of the competition with a shock victory over Arsenal at the Emirates and are now just 90 minutes away from a Wembley appearance.
Dann accepts that Blackburn remain outsiders to lift the trophy, but is determined not to let this opportunity slip by.
"You don't want to count your chickens," Dann told the Daily Mail. "If you look at the teams still in the competition, you'd be wrong to think it's going to be easy getting to the next round, never mind the final, then winning it.
"A lot of people will say we've got one of the more fortunate ties this round and they're probably right. We won't have a better chance in God knows how long to get to the semi-finals.
"But Millwall will be thinking exactly the same. They would rather play us than United, City, Chelsea, Everton or Wigan."
Dann was also keen to pay tribute to Blackburn manager Michael Appleton, who is the third man to lead the club this term after Steve Kean's unpopular tenure came to an end before Henning Berg's brief and ill-fated time at the helm.
He added: "When a big club like Blackburn drops down a league you need stability, and that's what the new manager has brought. The club have made a good decision bringing him in.
"He's steadied the ship, which was a bit up and down. He might have come in a bit late in the day to make a proper push for the play-offs, but given time I think he'll do a really good job."