Stortford responded with a number of chances, Alex Martin hitting Boaz Myhill's woodwork with the best of them.
Allsopp could have got another goal but failed to convert any of his chances, while Junior Lewis saw a header saved.
Five familiar faces in Ian Ashbee, Marc Joseph, Stuart Green, Stuart Elliott and Ryan France were brought on at half time, along with new signing Aaron Wilbraham. First team coach Steve Butler, who had played in the first half, and the impressive Keane were among those making way for the maximum six substitutes.
9 minutes into the second half, Wilbraham got a debut goal. His first shot was blocked but he made no mistake with the rebound to make it 2-0.
Andy Dawson was withdrawn with just over 20 minutes to go due to a hamstring strain, so the Tigers played out the rest of the match with 10 men. This was not to matter though as the home side were unable to threaten Myhill's goal.
City line-up (4-4-2): Myhill; Wiseman, Thelwell (Ashbee), Delaney (Joseph), Dawson; Fry, Hinds, Lewis (Green), Keane (Elliott); Butler (France), Allsopp (Wilbraham).