The Glovers rarely came close to breaking the deadlock against a County side who have now gone four games without scoring.
After 11 minutes Stockport's Tommy Rowe saw a shot blocked by Kieran Murtagh, then Chris O'Grady forced a fine save out of Chris Weale. Rowe also latched onto a cross from Michael Rose but he could only side-foot wide from close range.
Shortly before the interval Glovers' striker Gavin Tomlin wastefully drove a shot well over the crossbar from inside the box.
Four minutes after the restart Stockport were left cursing their luck when a downward header from young defender Josh Thompson bounced up and onto the crossbar before being cleared to safety.
Stockport's young midfielder Greg Tansey was denied by a superb save from Weale, and in the closing stages substitute Luke Rodgers blasted a decent effort over the bar for the visitors.