Watford, however, grew into the game and almost scored when Ben Mee diverted the ball into the direction of his own net from an opposition corner, but danger was averted after Aaron Lennon cleared off the line.
In a game devoid of genuine quality, Burnley came closest through Wout Weghorst when the Dutchman's deflected shot hit the bar early in the second half before the Watford frontline forced Nick Pope into a number of decent saves late in the game.
"It was a nervy game. The quality just wasn't there today as everybody was on tender hooks. The conditions were hard today," Watford keeper Ben Foster said, who kept the club's first clean sheet this season.
The result meant that both teams stay in the relegation zone, with Watford in 18th place on 15 points from 21 games, and Burnley two points behind in 20th but with a couple of games in hand.
Hodgson, who replaced Claudio Ranieri last month, added that the defensive improvement was "significant" given their long-standing woes at the back.
"We know unless we defend in the way we did today -- being compact and aggressive in our pressing -- then you won't get clean sheets in the Premier League. I thought this was a stern test... and I thought they dealt with it very well," the former England manager said.
Burnley boss Sean Dyche felt his side ended the game strongly but did not do enough to earn the three points.
"I thought we started brightly, lost our way a little at the end of the first half then regained it again in the second half. Maxwel Cornet has not played much for weeks and obviously Wout Weghorst is new so they are connections which will hopefully develop," he said.