The first half was a very even affair but the young Red Devils took the lead shortly after the restart, Charlie Savage's shot deflecting in off Yann Sanogo'o, and they went on to win 3-0.
It was not a result that had been on the cards at half-time.
"In the first half it was very even, a lot of possession in the game, both teams sussing each other out," reflected Adams.
"In the second half they scored an own goal from our point of view and quite quickly after that they scored the second. They took their goals very well.
"There wasn't a lot of goalmouth action from both sides but once they got a goal, they got a lift from that."
Bradford's lack of ruthlessness was in evidence again as they pushed for a goal from 2-0 down.
"We had balls in the box but as for most of the season we haven't been clinical enough," said Adams.
Their goalscoring problems were compounded when Caolan Lavery had to pull out of the XI with an injury suffered in the warm-up.
Theo Robinson is also out, leaving Andy Cook as the only senior centre-forward, and Adams did not want to risk him.
"He injured himself in the warm-up so I had to change it," said Adams of Lavery.
"I didn't to risk Andy Cook so early in the game, I really didn't want to risk him at all but I had no choice in the end.
"Theo Robinson picked up a knock in training the other day.
"We had Alex (Gilliead) in the first half and Kian (Scales at centre-forward) in the second but I just felt we needed to add another up front.
"Missing the game tonight would suggest both will be struggling for Saturday."
Cook came on in the 64th minute.
After defeats in their first two matches, Bradford's involvement in the competition will soon be at an end and Adams will not mourn it.
"When this competition's over and done with it's a lot better," he said. "We'd like to get through in the competition but we're probably not going to do that any more so we'll look to the league campaign."