Watford had recorded back-to-back victories but headed goals from Burnley’s club record £10.5m signing Jeff Hendrick and defender Michael Keane settled matters in the Lancashire outfit’s favour.
A second triumph of the season moved Burnley to 13th in the Premier League ahead of Arsenal’s visit to Turf Moor on Sunday, while Watford, who host Bournemouth at the weekend, stayed 11th.
“It was poor,” said Deeney. “I have to watch my words so I don’t get in trouble but we got bullied, all over the pitch to a man. Fair play to Burnley, they had a game-plan, they stuck to it and they delivered – we just didn’t.
“We got bullied and we didn’t reach our standards. We got run all over and both goals could have been avoided. I’m very disappointed.
“We’ve had the highs of the last couple of weeks, you set those standards and if you don’t match them then people have every right to ask questions, and so they should.”
Burnley opened the scoring seven minutes before the break as Hendrick soared highest in the penalty area to plant a downward header from Steven Defour’s corner beyond former Tottenham goalkeeper Heurelho Gomes.
Watford appeared a more lively proposition in the second period and England stopper Tom Heaton was forced to repel a stinging effort from Deeney.
But the Clarets doubled their lead five minutes after the restart when an inswinging Defour cross was glanced beyond Gomes by towering former Manchester United centre-half Keane.