The Owls created plenty of chances against visitors with little to play for in the final weeks of the season, but lacked a spark and a finishing touch.
They looked more threatening when Jordan Rhodes came off the bench to join Josh Windass, but the club record signing missed a string of chances.
It left Wednesday relying on Keiren Westwood's penalty save from Lewis Grabban at the end of the first half just to claim a point which put them in limbo for the next couple of hours.
"It looked like the occasions got to us maybe, particularly in the first half," admitted assistant manager Smith, again standing in for the ill Darren Moore.
"We still had chances but we didn’t get the three points and that what mattered.
"It was a great save from Westy for the penalty.
"We will have to wait and see what happens later. Hopefully results do go for us."
Wednesday were fortunate not to be punished for some sloppy defensive mistakes, the penalty coming from a poor defensive header by Adam Reach, and Grabban played in during the second half by a weak Julian Borner backpass, only for Westwood to force him wide.
"It's very frustrating," said Smith of the errors. "There was a lack of concentration but fortunately it didn't lead to us conceding goals."
Smith said the dressing room was disappointed at full-time, but not resigned to relegation.
"There isn’t a resignation there," he insisted. "We have to give it another push."
The game finished shortly before Derby County kicked off at Swansea City, and the Hillsborough stalemate meant Wayne Rooney's side just needed a point to relegate the Owls - although after five straight defeats for the Rams, that was far from guaranteed.
Rotherham United could also effectively send the Owls down by taking four points from their next two matches, but if not Wednesday are at Derby next Saturday in what would be a relegation decider.
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