Hornets captain Deeney, who scored 21 times in the promotion campaign last term, finally found the net for the first time since then when he put his side ahead with a low shot from fellow forward Odion Ighalo's clever tee-up in the 43rd minute.
And Flores said afterwards of the man he describes as the "soul" of the Watford team: "I'm really happy (for Deeney) and I wasn't worried about the situation.
"He has been working hard and is the soul of the team.
"But it is better for him because we know, for strikers and their confidence, it is very important when they score."
Deeney and Ighalo caused problems throughout for Stoke, with each hitting the crossbar seconds apart moments before the opener, and the latter subsequently providing another assist as he set up Almen Abdi to make it 2-0 with a strike in the 69th minute.
Flores added: "Both Ighalo and Deeney played really well.
"For us, it is very important how they keep the ball very well
They are always pushing the team
Their performances are always very important."
The result adds to what has been a very creditable start to the season for Watford, who now have 13 points from 10 games and are up to 13th in the table, a place and a point clear of Stoke.
"I'm really happy with the performance of the team," Flores said.
"We played really well today - with a lot of confidence
The balance of the team was amazing, and when we play like this it is very difficult for Stoke and for other teams also."
Stoke were guilty of errors when both goals went in, the first seeing Philipp Wollscheid slip as Deeney shaped to shoot and the second Ighalo feed Abdi having dispossessed Marc Wilson, who had come on early for the injured Geoff Cameron.
The Potters had gone into the contest on a three-match winning run in the Premier League and boss Mark Hughes admitted he had been left mystified by the performance his players produced on his 100th game in charge at the club.
"We were poor today, and credit to Watford," Hughes said.
"They came here with a good game plan and worked hard at it
They had a good threat up top with the two lads (Deeney and Ighalo) up front, who messed us around all day long to be honest.
"We needed to be better and we did not really see that performance coming
We have been playing well of late and getting good results.
"You have to put it down to individual errors, collective errors and the good play of the opposition."
Regarding Cameron, who limped off in the ninth minute, Hughes added: "It looks like he has pulled his thigh unfortunately
"I think it is fair to say that probably disrupted us, but we can't hide behind that
There were good players on the pitch today and we should have done better."
Source : PA
Source: PA