Striker Deeney hit the winner in the seventh minute of injury time - seconds after Manuel Almunia had saved Anthony Knockaert's penalty which would have sent Leicester through.
Instead Watford broke away and the ball fell to Deeney to crash in his 20th goal of the season and fire the Hornets into a showpiece match against either Crystal Palace or Brighton.
"I can't imagine a worse way to lose," Pearson said. "When you get a penalty you just hope he scores it - then what happened after that compounds the misery.
"Anthony is distraught as you would expect. I'm the first to admit it was a generous penalty decision. But to concede off the resulting penalty save is very hard to take.
"Unfortunately that's the nature of the beast."
The Hornets' promotion dream looked over when, with the teams tied at 2-2 on aggregate, Marco Cassetti nudged Anthony Knockaert in the area and referee Michael Oliver awarded Leicester a 95th-minute spot-kick.
But Almunia blocked Knockaerts' penalty, and the rebound, and moments later Deeney struck the knockout blow.
In scenes reminiscent of Doncaster's breakaway goal to win League One at Brentford a fortnight go - when the same referee gave the Bees a penalty - Watford charged upfield.
Fernando Forestieri swung in a cross from the right and Jonathan Hogg's header back across goal fell to Deeney, who thumped the ball home to spark wild celebrations.
- Sports & Recreation
- Anthony Knockaert
- Manuel Almunia