The Irish forward has had his troubles from the spot in the past, including a last-gasp miss in the opening-day loss to Liverpool, but he coolly slotted home 14 minutes from time after Laurent Koscielny had been penalised for handling in the box.
"That's what you'll get from Jon because he's mentally very strong" Hughes said. '"He's a senior player in the group and he takes responsibility each and every day.
"It doesn't surprise me that he grabs the ball, he wasn't going to give it to anyone else and I was really pleased for him that he was able to dispatch it because it was a pressure penalty, obviously."
The victory moved Hughes' side six points clear of the drop zone as the hosts continued their excellent home form against Arsenal, who have claimed just one win from their last 10 visits to Stoke.
But the Welsh boss felt that Arsenal could have no complaints with the result or the penalty call from referee Mike Jones.
"The stars were aligned and it came together," Hughes added. "I thought we were excellent on the day to be honest, going up against a very accomplished Arsenal side with a lot of talent and a lot of ability, but I thought we matched that and in the end we've won the game courtesy of a penalty.
"I've obviously been made aware that Arsenal felt perhaps it wasn't a just penalty, but honestly I'm a bit bemused by that, I felt it was clear-cut to most people.
"But regardless of that I felt we deserved the victory anyway by virtue of what we produced. All in all, a very satisfying result and performance."
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