Two goals inside two minutes by striker Matej Vydra gave the Hornets a thoroughly deserved victory following a goalless first half before a crowd of 26, 727 at the Amex Stadium.
Troy Deeney put the Hornets ahead nine minutes after the break when he fired low past keeper Tomasz Kuszczak following a pass by Daniel Pudil.
Spanish midfielder David Lopez pulled Brighton level 10 minutes later from the penalty spot after Tommy Hoban was penalised for bringing down Kazenga LuaLua.
But Vydra restored Watford's advantage with a deflected shot over keeper Kuszczak, before latching onto a through-ball from Deeney to fire the third with a classy finish.
"It was a typical game that when you are on top you need to score," Poyet said. "We failed to take advantage and then it was too open. We tried to address it at half-time but then they scored.
"We were lucky to get back at 1-1 but it was the turning point. We were not the better team.
"The second goal killed us off as Watford responded to the impact of us equalising. We didn't adapt very well and defensively we didn't adapt well.
"Watford's two strikers were much better as were their centre-halves. Inside the box we were second best. It was not a good day."