Town have scored just one goal in 500 minutes of football - poor final balls and woeful finishing costing them against Paul Tisdale's men.
Jamie Cureton could have put the visitors ahead after 15 minutes - Fleetwood goalkeeper Scott Davies denying the prolific striker.
Jon Parkin, Gareth Evans and Ryan Crowther all had half chances for the home side.
And they kept up the pressure after the break and Artur Krysiak was forced to save from a Parkin header.
Anthony Barry came closest to breaking the deadlock, his effort following a short corner appeared to be goalbound until it hit Evans, the Fleetwood winger just unable to get out of the way.
The hosts kept up the pressure but could not find a way through.
A late rally almost saw the Grecians snatch the points - Cureton and John O'Flynn seeing chances headed off the line before captain Danny Coles blazed over from six yards.