The Terriers made a bright start and Danny Ward's flicked header from Adam Hammill's right-wing cross gave them a 17th-minute lead but the advantage lasted just over a minute as Fernando Forestieri hit back immediately.
Troy Deeney played the ball out to Davide Faraoni who centred for the unmarked Forestieri to drive home into the bottom corner.
Two minutes before the break Watford scored what proved to be the winner. Hammill's needless foul on Forestieri conceded a free-kick just on the edge of the box. Lewis McGugan's strike was parried by Alex Smithies but he could not hold the ball and Daniel Pudil slotted home.
Robins said: "For the first 20 minutes we showed how good we are but after that Watford came at us.
"We gifted the two goals and were on the back foot after that. For their first goal they broke really quickly and the finish from Forestieri was Premier League quality.
"We have to believe in ourselves, keep the ball better and be patient.
"We have lost our unbeaten home record to a good side."
Robins brought on 18-year-old academy midfielder Duane Holmes for only his third appearance at half-time.
He is taking it carefully with the teenager and said: "He needs the experience and this was another 45 minutes under his belt. He made a difference when he came on and eventually he will start hurting players.
"We will keep looking at him and see how he develops."