The Barclays Premier League side were gifted a 1-0 win as United defender Scott Wootton put through his own net after 53 minutes.
And Flores believes the Hornets, who have been so impressive on their return to the top flight, can now turn their attentions to a first FA Cup final at Wembley since 1984.
"It is important to permit the fans dream every time," said Flores, whose six changes included giving star man Odion Ighalo a rest.
"We are living an amazing experience in the Premier League, an amazing season in the FA Cup and have a very professional attitude from the players.
"The fans are supporting our football and style, so they need to dream, and we support their dream because football is for love and to create dreams."
On a wet and blustery day at Vicarage Road, Watford, who are yet to win football's oldest club competition, started the stronger of the two teams.
But as the opening period wore on Leeds, who ended the day 17th in the Sky Bet Championship, started to take control without creating any clear-cut opportunities.
Watford emerged with greater determination in the second period and the breakthrough came when Wootton, the former Manchester United academy player, shanked the ball into his own net following a cross from Ben Watson.
"I think we had the possibility to score before the own goal as we created very good attempts," Flores added
"The cross from Watson was amazing - football is football.
"I am really pleased with the performance of the team
We play really serious, in a professional way and respecting Leeds.
"The most important thing is to be competitive because Leeds were a very difficult opponent, strong in defence and very organised.
"So, we are now thinking our next target is Bournemouth in the league - we need to enjoy with the fans this victory - but tomorrow we will think about the next competition."
Wootton held his head in his hands after he attempted to direct the ball for a corner, only for it to instead nestle into the bottom corner of his own net.
"He was distraught on the pitch and he was standing by the door shaking hands and apologising to every player and member of staff," Leeds manager Steve Evans said.
"There is nothing that anyone can say to Scott Wootton that will make that kid sleep for a day or two, so I really feel for him.
"If he gets that 100 times, he deals with it 99
It is a mistake, an error and no player in the world goes to do that, but I don't think you need a shout there
He should deal with it
It's a particularly cruel way to go out."
Source : PA
Source: PA