The Gunners yet again came unstuck at the bet365 Stadium through a strike from debutant Jese Rodriguez early in the second half, having dominated the opening 45 minutes.
Arsenal managed 18 shots in total, six of which were on target - not including Alexandre Lacazette's offside goal - but they were unable to legally find a way through at a ground where they notoriously struggle to perform.
"It's a difficult defeat to swallow. We had chances - we should have won the game comfortably," Wenger told BBC Sport. "We were unlucky. I think we scored a regular goal that was given offside and it wasn't offside. It was frustrating getting caught cold for the goal.
"Defensively there is no excuse. We gave them a cheap goal. It was difficult to get the fluency. We tried but we couldn't find the goal. There was lack of anticipation in the box with the second ball. To lose a game like that is disappointing. You don't want to lose games that you should win."
Stoke have lost just one of their last eight league meetings with Arsenal in the Potteries, with that solitary defeat coming last season.