The Hornets beat Arsenal 2-1 at the Emirates Stadium on Sunday and will now face either Crystal Palace, Everton, Manchester United or West Ham United in the final four at London's Football Association headquarters.
Flores, who guided Atletico Madrid to the 2010 Europa League title, admits it is the most significant occasion of his managerial career to date and spoke with pride after his players did the job in North London.
"I think this is the most important moment of my career," the Spaniard said.
"We try to enjoy this moment, this journey, this team, we now get to play in the semi-final at Wembley.
"This season is an amazing season for Watford, the players play for the fans. This is the necessary impetus we need for the remainder of the season."
Second-half goals from Odion Ighalo and Adlene Guedioura had the Hornets in pole position before Danny Welbeck pulled one back in the 88th minute.
The visitors then survived a late onslaught which saw Alex Iwobi hit the post and Welbeck fird wide with an open goal beckoning in injury-time.