Jonny Howson netted in the 34th minute at the Britannia Stadium with a strike from outside the box as the Canaries took advantage of some sloppy play by their opponents.
Norwich had already hit the crossbar through Ryan Bennett and were good value for their lead, but they survived a nervous moment after the break when Leroy Fer appeared to pull back Kenwyne Jones in the box, with no spot-kick being given.
Regarding the Jones incident, Fer confessed after the game that he had "pulled his shirt a little bit".
And when that was put to Hughton, he said: "He (Fer) is an honest lad!
"I have seen the incident, and yes, there is contact - I have to say, I thought the lad (Jones) made a meal of it.
"But if it is something we have got away with, then I think we are due one, as all Norwich supporters will tell you."
The victory was Norwich's second in the league this season, giving them seven points from six games and moving them up from 17th to 14th in the table.
It was also only their second top-flight away win in 2013 - the other being a 3-2 triumph at Manchester City in May - and Hughton said: "I think every win away from home is a big win, particularly for us, given we have found it more difficult away from home.
"I don't think there is anyone who would say different than we thoroughly deserved it. It is a big lift."
Norwich went on a considerable spending spree over the summer and there had been talk in the build-up to this contest of Hughton being under major pressure to get a positive result against Stoke.
Asked about that, Hughton said: "It comes with the territory. If we are talking about managers, there will be nobody that puts them under more pressure than themselves, because we take every defeat heavily.
"Of course, the burden of results is always on you as a manager, but you have to be able to cope with that and have belief - if you didn't have belief in your own ability and what you can do with the team, then you wouldn't take the job in the first place.
"You have to be calm through any periods of pressure, or supposed pressure, because it is about the players not feeling it and getting a result.
"Has there been a little bit more additional pressure? There has, because before the game, we were sitting fourth from bottom and that is pressure in itself."