City made it two wins out of two in this season's competition after first half goals from Haris Vuckic and Jordy Hiwula helped to secure a 2-1 victory over Bury at the Northern Commercials Stadium.
The Bantams now only need a single point from their final Northern Group C match away at Morecambe next month to secure progression into the knock-out stages.
Tuesday's encounter with Bury saw Nathan Clarke and Rory McArdle both make their first appearance of the season for the first team, while Daniel Devine and Filipe Morais also got important match minutes under their belt.
Black, who once again led the side in this competition, said: "We were certainly keen to keep the momentum going from our recent league form.
"We've had back-to-back victories in the league and now we've had back-to-back victories in this competition.
"Certainly in the first hour, I think we played some really good stuff.
"We were delighted to see Haris (Vuckic) get his first goal. We were delighted also to see Jordy (Hiwula) get a goal because he probably deserved one at Chesterfield on Saturday.
"It was good to have Nathan (Clarke) and Rory (McArdle) back.
"Nathan actually got quite a bad blow to his eye in the first half and it was very swollen up by full time so he showed a lot of character to play on.
"Danny (Devine) has been out of the side for a bit but he slotted in nicely with Tim (Dieng) in that midfield and they looked very promising.
"He is certainly an option we have for Saturday (vs Shrewsbury Town) with Josh (Cullen) being away with the Republic of Ireland U21s.
"It was important for these players, along with the likes of Filipe Morais and Matt Kilgallon, to get ninety minutes tonight (Tuesday).
"The lads naturally want to be playing in the league games but they realise that they have to be patient for their chance.
"Their attitude in training has been spot on because they know they have to be ready at the drop of a hat to come into the side and perform if needed."