Emery’s side were not at their best as they were outplayed by the Hornets before a late Craig Cathcart own goal and a Mesut Ozil strike secured the points.
The win was a fifth in a row in the Premier League, with victories in the Europa League and Carabao Cup adding up to an impressive run for the Gunners.
After losing their opening two fixtures under Emery – against Manchester City and Chelsea – Arsenal boast a 100 per cent record since and Holding praised the new head coach for his approach.
“He said when he came in that he wanted to bring a winning mentality and I think you get that from wins and you go into each game confident,” the defender said.
“We’re physically fit and we know that we can go and get the result. It was a really competitive and physical game and we knew that coming in.
“We just had to stand up to the battle and late on I think they tired and we managed to get a few passes together and score the goals.”
Watford made the short trip to north London defending an unbeaten away league record.
Javi Gracia saw his team create enough chances to win the game, captain Troy Deeney forcing a fine save out of substitute goalkeeper Bernd Leno and Isaac Success clipping the post moments after coming off the bench.
They were then hit by the sucker punch of an unfortunate Cathcart own goal, the defender unwittingly turning Alex Iwobi’s cross past Ben Foster.
The points were secured by the hosts just two minutes later as Ozil was in the right place to steer home Alexandre Lacazette’s ball into the box – with Watford midfielder Abdoulaye Doucoure left ruing missed chances to take the lead.
“We played 80 minutes very well,” he told the club’s official website.
“We defended well and created chances but we didn’t score and against this type of team we know you have to score first.
“At the end we lost and we are very disappointed. We knew before the game it would be tough, we let them score first and it was very hard on us at the end.”