The Eagles went into their play-off semi-final against rivals Brighton on the back of a miserable run of one win in 10 matches, and the in-form Seagulls were big favourites to progress at the Amex following a goalless first leg.
But two goals from Wilfried Zaha booked Palace a trip to Wembley to face Watford in the final a week on Monday.
The Hornets will be fancied to secure promotion, though, having finished five points ahead of Palace and taken four points off them earlier in the season.
But Speroni is confident Ian Holloway's side can spring another surprise in the showpiece reckoned to be worth around £120million to the winners.
"It doesn't matter what anyone else says, we probably were the underdogs but we didn't care about that, we just went to play our game," said the Argentinian.
"People talk about momentum going into the play-offs, but it's about what happens on the day.
"It doesn't matter what happened in the season. It's one game and Watford will we very tough opposition. It's all about what happens on May 27.
"I didn't think we were underdogs against Brighton, but people say that about us. Even if we'd lost the first leg we still had a chance, the Championship is so competitive.
"But we don't care, and to be honest I think it's 50-50 for the final."