The game was nearly won by Chris Brunt just minutes before spot kicks decided the contest when the winger crashed a free-kick onto the post.
Adam Proudlock gave The Owls the lead before Watford hit back through Hameur Bouazza as the scores finished 1-1 in 90 minutes.
The Owls notched penalties through Brunt, Guylain Ndumbu-Nsungu, Jon Shaw and Lewis McMahon but Matt Hamshaw's final kick was saved.
Wednesday were knocked out of both the League and FA cups last season on penalties against Hartlepool and Scunthorpe respectively.
Patrick Collins was the only change in the side which beat Preston on Tuesday, he replaced Graeme Lee at the back.
Left-back Paul Heckingbottom is now looking forward to the start of the season after the tripto the 'White Island', he said: "We have had a couple of games out here in Ibiza and then we go back and then they start to come thick and fast.
"But before you know it, you are at the start of the season and that is what we are all aiming for."
A Wednesday XI take on Barrow on Tuesday before another away trip on Saturday week when The Owls face York.