A Pascal Gross brace and Tomer Hemed strike saw them notch their first goals in the league at the fourth time of asking in a 3-1 success over West Bromwich Albion at the Amex.
It was an accomplished performance against Tony Pulis' side that went into the match unbeaten so far this season.
Hughton also admitted that after the game he could take a sense of relief from what was Albion's first win in the top flight for 34 years.
The Seagulls boss said: "When you are on the back of a performance (at Watford) that you think should be a winning performance, it is always really pleasing when that happens.
"I thought we thoroughly deserved it, although it was a difficult end to the game, but that's normal once they get the one goal back and it becomes a bit nervy, but I thought we coped with their threats very well and were very good on the ball.
"I must admit, it didn't feel before that game that we needed a bit of relief, but I suppose that is the case. We are four games into the season and we want to get that first win, it's a worry if you don't.
"I think I have a group of lads here that are realistic enough to know it is going to be a tough season, but certainly there is a really good feeling at the moment having got that first win under our belts. And not only scored three goals, but arguably got in some good enough positions to perhaps have got more.
"We know Tony's team and they are very good at what they do and they don't give you much space. It was about trying to get space behind their shape and I thought we managed to do that.
"I think we have had a lot of key moments in my time here at this club. If I look at the exploits they were massive at the end of last season and that went on for quite some time. It is only then that for this club you understand the magnitude of it.
"We got to 70 minutes against a very, very good Manchester City side and if we had managed to hold out that would have been been a massive key moment in the season. Last week was and I think again today was our first win, we have to keep looking at getting those key moments."