Ismaila Sarr, who had not scored since the opening-day win over Aston Villa, proved too good for the Norwich defence with his brace putting the game beyond the hosts.
The Hornets had taken an early lead as Emmanuel Dennis headed past Tim Krul after being marked poorly in the 17th minute but Norwich levelled through Teemu Pukki before the break.
However, in the second half, Watford took a decisive lead in the 63rd minute with Sarr beating Grant Hanley to the ball before flicking it into the net and then being first to a parried shot from Josh King to tap home for his second 10 minutes from time.
“[It’s a] tough day,” Farke admitted. “It’s also tough to take because first of all we wanted to make a mark. In general football is quite an awful thing.
“It was a tight game, 50 per cent possession and 12 shots on both sides and we had three really crucial mistakes in our defending game.
“I think that wasn’t clinical enough in our own box and of course the goals change the momentum of the game and the situation, it was not one situation.
“If you produce these mistakes on this level you are punished and then we were not clinical enough to earn the right to win the points.
“In these moments you have to be self critical, it was not a tactical problem, there was not one situation where we were overloaded [in terms of player numbers] but we should have defended much better.
“If I’m honest [there were] too many defensive mistakes in order to win the game.”
Norwich had the toughest of starts – against Liverpool, Manchester City, Leicester and Arsenal, but again struggled against their fellow promoted side and have now lost five successive matches against the Hornets, with Farke insisting there were improvements needed.
He added: “[We have to] roll our sleeves up and work on it, individually but also as a team on the training pitch.
“Of course this is something we have to improve because we have conceded too many goals so far.”
Watford manager Xisco Munoz praised Sarr for his performance and insisted the 23-year-old is happy at the club.
He said: “I feel he is very happy here and he enjoys every day in training and he gives very good things for our team. Sarr was very good but not only Sarr.
“We were mature with the ball, without the ball and we managed the timing of the game. It’s perfect because it’s one step forward.”