Former Clarets striker Andre Gray put Watford ahead after three minutes, before Dyche's side rallied back and equalised in the sixth minute from a corner - with defender James Tarkowski getting his first goal of the game.
Despite controlling the remainder of the first half, Burnley found themselves on the receiving end of two quickfire goals at the start of second period from Troy Deeney and Will Hughes.
Speaking after the loss in the post-match press conference, Dyche said: "We gave the game away. In the very beginning we were not very sharp - their first shot on target goes in.
2012: Takes over at Burnley, they're 14th in the Championship— bet365 (@bet365) August 16, 2018
2014: Promoted to the Premier League
2015: Relegated from PL
2016: Win the Championship
2017: Finish 16th in PL
2018: Finish 7th, qualify for Europe
2018: 180 minutes from Europa League group stage
Sean. Dyche. pic.twitter.com/Xf5GsCVZHH
"We responded very well, had a good first half and a number of chances we should have made more of.
"The players had a warning to start the second half right and we didn't. The only gripe is that you can understand if we didn't start well but the players had that warning before the second half."
The match gave Watford their first Premier League away win since November 2017, as well as scoring their first away goal since January.
Setting his frustrations with his team aside, Dyche and Burnley now look towards a midweek trip to Greece to face Olympiakos in the first leg of their Europa League playoff clash.
The Clarets then return to England for a Premier League clash away against Fulham at Craven Cottage on Sunday.