"It's a little bit of relief on the back of some really tough games and our performance and the level of our performance hasn't been that bad, but of course we're on the back of two defeats to the two Manchester clubs," he told Sky Sports News.
"It was good firstly to come back home here and of course to play one of the sides that are not one of the top teams, and I thought we thoroughly deserved it in the end."
Hughton added that Norwich now need to "build on" their win against the Hammers.
"Sometimes when you're on a run like we are, there's a little bit of nervousness," he said. "What I did see was West Ham score a goal, but I can't think of a real good clear-cut chance that they had in the first period and I think that's the most disappointing thing.
"We were certainly able to raise it in that second half and apart from the goals I thought we had some other very good chances. We have to build on this.
"We had a similar start last season where we had some tough games and didn't start so well, and we had a game here against Arsenal and from then onwards we were a better side. It was a bit of a spring forward and let's hope that's today."
Norwich are currently 15th in the league table with 11 points from as many matches.