A Ryan Yates own goal handed Braga the 1-0 win, with Morgan Gibbs-White failing from the spot for the visitors just a minute earlier. Forest midfielder Elliot Anderson was also sent off in injury-time.
Dyche lamented afterwards: "Very frustrating. I saw one minute of madness in a game where we never really looked in trouble. We didn’t dominate as much as we hoped, or open them up as many times as we hoped.
"Also playing without a recognised centre-forward can make it tricky. We miss a penalty, but that can happen, and then the reaction is nowhere near good enough for the next minute or so and we lose the game to what is a really poor goal.”
The Forest manager also stated: "You see it happen, they get a lift, the crowd go mad. We knock off for a minute, go chasing the ball, they get lucky with a bobble into the box and that can happen. Then a unfortunate situation for Ryan Yates.
"Very frustrated. I think the tempo of the game - we got sucked into playing slow. Didn't really affect the back line as many times as we hoped. We got the penalty, and it is one of those games if you seal that."
Dyche continued: "We want to do well in this competition, we still do, of course. They are working ever so hard in training. To come here, we expect to step on and that is the kind of thing we are waiting for, that feeling to take the game on, and it never really occurred.
"You might come away with a draw, but you shouldn't really lose that game. One minute of madness cost us the game. I don't think they had a real chance, then we had a goalmouth scramble and even that can't go in."