Ben Reeves had the first chance of the game, firing in a volley which forced the Coventry goalkeeper, on loan from Bournemouth until January, into a smart save in the 12th minute, after Dean Bowditch had his fumbled attempt closed down well.
Bowditch went close again midway through the first half, but saw his precise lob headed off the goal-line by Reda Johnson.
The visitors finally threatened shortly after the restart when Jordan Clarke volleyed agonisingly wide from a City corner.
But Allsop was the far busier of the two stoppers and he did well to palm away a Reeves effort from the edge of the box in the 64th minute.
And lady luck was also smiling on the former Leyton Orient stopper who saw Daniel Powell fire a powerful effort over the crossbar, before Reeves hit George Baldock’s cross off target late on.