The Gunners conceded in the 76th minute when Jon Walters' flick struck Laurent Koscielny's arm in the box and referee Mike Jones awarded a penalty, which the Potters forward stepped up and converted himself.
Wenger described the goal as a "nice gift" for Stoke from Jones, but was also in no doubt that Arsenal had not been good enough in attack during the contest.
And with the result, plus leaders Chelsea's 3-1 win at Fulham, meaning Arsenal are now four points adrift of the Blues with each having 10 top-flight games to go, Wenger said: "It is not slightly worrying - it is a big worry for us to lose a game like that
It is a massive setback.
"It was a good defensive performance and, overall, we were unlucky to lose this game
But offensively we didn't create enough
"Our offensive game was poor, considering our standards
And, at the end of the day, we didn't score because of that.
"We conceded a goal which was a nice gift from the referee, but that can happen.
"He is one yard away - how can he take his hand away? He has no time to take his hand away from the ball.
"He had no intention at all, but we cannot influence the decision of the referee and I feel going forward we were not good enough to create chances, and that is why we were punished."
Wenger insisted his team are "not fragile at all", and, on the prospect of them bouncing back, he said: "I'm not worried.
"But we didn't produce the performance we wanted and to win a title, when you are expected to perform, you have to perform
It is as simple as that."
Arsenal striker Olivier Giroud in particular was on the end of some rough-looking treatment during the game, with Stoke midfielders Glenn Whelan and Charlie Adam appearing to stand on the France international.
Wenger after the match made reference to the Potters' physicality, but was reluctant to speak about individual incidents.
He said: "You have to give credit to Stoke
They defended well, with resilience, and made the game very physical.
"We knew that would be the case before the game, though
They have the highest number of fouls in the Premier League
But we didn't cope well enough with it and at the end of the day we were punished."
Asked about the challenges on Giroud, Wenger added: "I don't want to talk about the referee
I have nothing to say about that.
"I am long enough in the game to make my own judgement and I prefer to concentrate on our own performance."
When questioned about Adam in that context, Stoke manager Mark Hughes said it was the first he had heard about it, adding: "It would be a shame if people highlight that as it wasn't that type of game."
Hughes, whose team are now six points clear of the relegation zone, was keen to praise the Potters' efforts in achieving what was only their second victory in 11 Premier League games.
Reflecting on a result that sees Stoke's record at home against Arsenal extend to one loss in the last eight, and follows other notable victories this term in triumphs against Chelsea and Manchester United, Hughes said: "The stars were aligned and it came together
I thought we were excellent on the day to be perfectly honest.
"We were up against a very accomplished Arsenal side with a lot of talent and lot of ability, but we matched that and in the end won the game courtesy of a penalty.
"I've been made aware that maybe Arsenal felt it wasn't a just penalty, but I'm a bit bemused by that as I thought it was clear-cut to most people.
"Regardless of that, we deserved the victory anyway by virtue of what we produced in our general play
All in all it was a very satisfying performance."
Walters has seen several of his penalties fail to hit the back of the net, and regarding his success this time out, Hughes said: "That is what you get from Jon - he is mentally very strong.
"He takes responsibility every day so it didn't surprise me that he grabbed the ball, he wasn't going to give it to anyone else.
"I was really pleased for him that he was able to dispatch it as it was a pressure kick.
"Charlie (Adam) wasn't too happy that I took him off as he sensed he would get a penalty
But he will get over it."
Source : PA
Source: PA