The hosts started well and their best opportunity came when the ball reached Junior Quitirna, whose and his acrobatic kick hit the post before being cleared off the line.
But, they came to rue their missed chances when Shrewsbury took the lead with their first shot of the game.
A mistake from Scott Robertson put Daniel Udoh one-on-one and he easily scored.
Before half-time Fleetwood goalkeeper Jay Lynch was shown a red card for bringing down Ryan Bowman.
After the break, Salop made the most of the extra man with Carl Winchester driving into the box from out wide to force a save from substitute goalkeeper Stephen McMullan.
However, Fleetwood responded when Jack Marriott poked a cross into the back of the net but the flag was up for offside.
The Cod Army continued to push but then lost Josh Earl late on to another red card in stoppage time.
Report supplied by PA Media.