First Aaron Ramsey smashed in his seventh goal of an impressive season after Mesut Ozil's fifth-minute free-kick was parried by Stoke goalkeeper Asmir Begovic, but Geoff Cameron swept in a deserved equaliser for the visitors.
However, the class of Ozil - signed from Real Madrid on deadline day in a B£43million seal - proved the difference as his corner was flicked home by compatriot Per Mertesacker to give Arsenal the lead once more before half-time, and then another pin-point deadball delivery made sure of all three points when Bacary Sagna looped in a header to make it 3-1.
"We showed courage to get back into the match after the early goal," Hughes said.
"We talked about trying to stay in the game in second half, and creating more opportunities for ourselves, and that is what we did with a level of control, but the third goal took the wind out of our sails."
The Stoke boss added: "Arsenal are a good team and have added a top-class player in Ozil, who had an influence today and I am sure that will continue."
Hughes was, though, less than impressed by the performance of referee Mike Dean and his assistants Gary Beswick and Jake Collin.
The Stoke manager said: "All people can have poor games and I think (Collin) had a poor game.
"I just felt his interpretation of some of the free-kicks and decisions which were given, both for and against (us)... I have seen that group of officials have better games, let's put it that way."