Adams' side started the contest on top, but two quickfire and composed Joao Carvalho strikes thwarted the Bantams’ first half performance, with hope lacking heading into the second half.
However, a spirited Bradford second half saw Callum Cooke net an audacious free-kick, but it wouldn't be enough to save the Bantams as their EFL Cup run came to a stop at the first hurdle.
Following his side's defeat at the hands of Nottingham Forest, Adams addressed the media, saying:
"Even though it ended in defeat, and we are disappointed to be out of the cup, we played very well overall.
“We began on the front foot, but unfortunately did not take advantage. We passed the ball well and got into some promising positions on plenty of occasions. The difference on the evening was the fact they were clinical and took their opportunities.
“To have that number of attempts and cause that much of a threat against a team two divisions above us was certainly encouraging. If the players continue to perform like that, I have no doubt the results will certainly come.”
With Bradford yet to win a game on their return to competitive football, there is yet to also be a return to Valley Parade, where the Bantams play next Saturday.
“We now look forward to what will be a fantastic occasion this weekend.
“Having our supporters back in the stadium is going to be a great moment for everyone at the club, and one we are all excited for.
“However, as great as it will be, we have to focus on winning the game which will not be easy, especially with us having two matches in a short space of time.”