Watford boss Javi Gracia felt they deserved more from defeat at Everton.
Bernard's goal after just 10 minutes was enough to give Everton their first victory of the 2019-20 season.
Gracia, speaking to BBC Sport, said: "I think today we had our performance and we were close to getting a better result.
"They scored from a long ball, an individual action. We were a little bit unlucky because our defender touched a little bit their shot. We then hit the crossbar, we had good performance but didn't take the chances and they won the game.
"We need to improve many things but there were many positives today."
Danny Welbeck made his Watford debut as a second-half substitute, and while the former Manchester United and Arsenal player made little impression, Gracia will be hoping the 28-year-old England striker will be up to speed soon to give some much-needed cutting edge.
The Watford manager added: "I am happy for him because he was a long time injured and today was his first game. I am happy with his performance and I am sure he will help us in the future."