The hosts were twice on the scoresheet but they were ultimately outgunned in the West Midlands by an impressive Red Devils outfit, with both Alejandro Garnacho and Mani Norkett hitting hat-tricks.
Sam Mather's 13th-minute opener was swiftly cancelled out by a tidy Kieran Wakefield finish in what was a fast start from both teams, as Jobe Bellingham also went close for Blues early on.
However, three further strikes from the visitors saw them hold an advantage at the interval, as Norkett found the net twice in as many minutes midway through the half before Garnacho opened his account for the game.
Having already claimed an assist for Wakefield's goal, Harry Manton got himself on the scoresheet soon after the break to bring the deficit within two and Callum Sullivan nearly made things very interesting when he was denied by Eric Hanbury in the visitor's net.
Instead, United responded emphatically and went on to match their first-half goal haul. Garnacho hit a quickfire double in minutes 73 and 75 to complete his treble. Malachi Sharpe then made it seven ahead of Norkett signing off the scoring with his own hat-trick effort late on.
Speaking after the cup encounter, Martyn Olrenshaw was keen to emphasise the lessons that his players will learn from the defeat.
He told BCFC.com: "We made too many errors in my opinion which led to their goals. One thing that we didn't do well is defend against the strength of their counter attack. Five of their eight goals came about this way and we weren't able to execute our game plan.
"It was a big drop off in performance levels, we felt the week's build-up had been good but we just didn't quite reach the same levels as we did against Tottenham Hotspur and Chelsea.
"If we are not in a position to win a game anymore then we need to learn how to manage those situations."
Blues are back in action this Saturday, with the team travelling to Arsenal as they return to league action.
Blues: Brooks, Sullivan (Oni 75, Barratt (Ogor 46), Nguepissi, Browne, Manton, Patterson, Khela (Oduka 70), Hall, Wakefield, Bellingham.
Substitutes not used: Rushton.
Goalscorers: Wakefield 15 and Manton 50.