Goals from summer signing Jeff Hendrick and key defender Michael Keane did the damage for Burnley but it was at the other end where goalkeeper Tom Heaton and his defence denied a Hornets side who had scored seven goals in their two matches prior against West Ham United and Manchester United.
"If you keep clean sheets, then you are going to have a chance in games," said Dyche.
"We did well the last time around (when in the Premier League) - we did not score as many, but if you look at the goals against, we did pretty well for a team that had come up and had a challenge on their hands.
"So we believe in the shape of the team and there is good organisation in the team, we know we have to be productive in the top third and that is our big challenge going through the season.
"But we have made a really solid start to the season."
Burnley now sit 13th on the top flight table with two wins and a draw from their opening six matches.