The hosts almost took the lead after just eight minutes when Sam Winnall ran onto a Paul Hayes pass to volley a fine dipping effort towards goal, but Scott Davies pulled off an equally impressive save to tip it over the bar.
Fleetwood began to push for the opener as the first half wore on, but they were wasteful in front of goal on a number of occasions.
David Ball was particularly guilty of not being clinical enough, firing a volley wide midway through the half before squandering a fine chance right on the stroke of half time with a scuffed shot that rolled harmlessly wide.
Ball had another chance six minutes after the restart, but this time he couldn't keep his shot down, putting it over the bar from a tight angle.
Gary McSheffrey almost opened the scoring in unorthodox fashion shortly afterwards when his corner nearly caught Davies out, but the Fleetwood keeper recovered in time to tip the set piece away.
The visitors were handed a golden opportunity to take the lead just after the hour mark when the referee controversially pointed to the spot after deeming that Terry Hawkridge had fouled Charlie Taylor inside the box.
Steven Schumacher stepped up to take the penalty, but Sam Slocombe produced a stunning stop to deny the striker from 12 yards.
Schumacher was called into action again 10 minutes later, this time denying Antoni Sarcevic's powerful volley from a tight angle.
The hosts had a rare shot on goal late in the game when Paddy Madden unleashed a fierce effort from the edge of the box, but Davies was equal to the effort as the match ended goalless.