The Eagles dominated possession and created the better opportunities in the second-round tie, but forward Jean-Philippe Mateta was guilty of failing to make the most of three good chances before half-time.
Christian Benteke replaced the Mainz loanee during the second period, but he was denied by Ben Foster with quarter of an hour left before Ashley Fletcher, on his full debut for the Hornets, provided the sucker-punch with a goal from close range in the 86th minute.
It made it three competitive games without a win for Premier League rookie Vieira, who has also seen his team not score this season.
“We have to change our mentality when we are in the opposition half. We have to be more aggressive and determined to take those chances because today we didn’t do it,” he said.
“There is a lot of frustration on our side because I think we created enough to win. I am disappointed because up front we have to improve ourselves. If we want to win football matches, we have to score goals and this is not the case.”
The 45-year-old spoke prior to the campaign about the need to bring in another forward, but with the transfer window due to shut in a week, time is running out despite the best efforts of chairman Steve Parish and Dougie Freedman, the Eagles’ sporting director.
Vieira added: “There is always two ways to watch games. There is the performance and today was good, but we missed some important parts and one of them was taking the chances.
“We need to have more conviction when we are doing things in the opposition box and at times we were a little sloppy. This is what needs to change.”
Watford boss Xisco Munoz was delighted a stronger performance after the break was rewarded late on to edge a typically high-tempo encounter between two teams who have plenty of history since the 2013 Sky Bet Championship play-off final at Wembley.
After making seven changes following Saturday’s defeat at Brighton, the Spaniard was happy to keep a clean sheet.
“I think we understand what is happening in the game because we knew we had difficult situations and we had balance,” Xisco said.
“The last games we conceded a lot and today we had more balance. We also had two or three chances in the game but it was important to wait for the moment to take our chance.
“We can give a better performance with the ball but it was a moment to improve our situation. Well done to the guys.”