Second half goals from Morecambe duo Paul Mullin and Cole Stockton handed the hosts victory but a double from the influential Haris Vuckic ensured City finished top of Northern Group C and will receive a home draw in the next round.
Youngsters Ellis Hudson, Tom Windle and Sam Wright all featured during the game, with Hudson and Windle starting, while second year professional James King was handed his senior debut in central midfield.
Black, who once again took charge of the team in the Checkatrade Trophy, said: "We're obviously disappointed with the end result.
"We had lots of pleasing play on show during sections of the game and we scored two good goals.
"We know Haris's quality from his time at Rangers. He will be disappointed by Saturday (vs Accrington Stanley, Emirates FA Cup) but he's come out in this game and produced the goods.
"We went one goal up but then found ourselves 3-1 down after a 10-15 minute mad period.
"The third goal we couldn't really do too much about because of the deflection but defensively we could probably do better with their first two goals.
"With Morecambe knowing before the game that they needed to win to qualify, we knew they would come at us after we scored but it could have been a different game if we'd hung onto our lead for a bit longer.
"It has been a good exercise for some of our younger lads tonight (Wednesday) and we've still managed to top the group, which was the ultimate aim."
Wednesday's game at Morecambe saw the welcome return of James Meredith from injury after missing the last four games with an ankle problem.
The Australian left back managed 69 minutes before being replaced by apprentice defender Sam Wright.
Black added: "We were keen to give him as long as we could.
"We wanted to give him at least the first half. I asked him how he was feeling at the break and it was positive so we gave him another twenty minutes.
"It was certainly very pleasing to have him back and, touch wood, he has come through the game unscathed and with no reaction."