The scoresheet was dominated by a hat-trick from Chris Wood.
Nuno said afterwards: "After what happened last week (5-0 defeat at Bournemouth) the answer today was good. Get punched, you get up. It was fantastic. These results are not normal in the Premier League, there is always a reason. Last week we were not good at Bournemouth, they were ruthless, and it happened today with us and Brighton.
"We had a bit of luck for the first goal, and there was a moment that they had a one v one against our keeper, there was a chance off the post, that was them looking to respond. We got lucky but after that we controlled the game very well.
"It is good to have the routines and habits and relationships that the players are developing more and more. They are getting to know the spaces better. Anthony (Elanga) was amazing today.
"We don't look at the table. What we talked about before the game was a clear message: We get beat, we get up. If we get beaten today we get up next week, that is the most important message for the boys.
"I don't know (about any late transfers). We have been focused on this game, now we will see in the next few days. The more important thing is the players that are here and happy, which you see in the way that they celebrate the goals of each other and as a team. If we can add someone that brings something that we are missing then we will try to do it."
Nuno added, "(The support) is great and we cannot thank them enough. It was beautiful to see the atmosphere at the City Ground, seeing our fans happy is what we work for and at the same time seeing our players, the way they celebrate the other players' goals, it's important. It's important for us that we keep this team spirit and try to build. We are confident going forward."