Their 2-1 victory over Tottenham Hotspur last weekend ensured Gracia's side are the first in the club's history to record four straight wins at the start of a top-flight campaign.
"I am very pleased," Gracia told the Premier League website. "We are enjoying (it). You never know what will happen.
"Don't look only at the end of the road. Try to enjoy day by day. Try to enjoy the very good atmosphere, the workers who are helping us, the supporters in all the games are amazing.
"I think altogether we can achieve very good things."
It is Gracia's first Premier League manager of the month award and the second to be won by a Watford boss after Quique Sanchez Flores in December 2015.
He beat Liverpool's Juergen Klopp, Spurs' Mauricio Pochettino and Chelsea manager Maurizio Sarri to the award.
Watford are one of the three Premier League teams with a 100 percent record this season, alongside Liverpool and Chelsea.
Tottenham Hotspur winger Lucas Moura became the first Brazilian to win the Premier League player of the month award since David Luiz in March 2011.
Moura scored three goals for Spurs last month, including a double in a 3-0 win over Manchester United at Old Trafford.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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