A double from Bryan Mbeumo and goals from Matheus Cunha and Casemiro helped United secure a third consecutive Premier League win for the first time since August 2024, before Amorim had taken charge.
There were nervy late moments as Brighton mounted a comeback at Old Trafford, but United held on to build on their first Anfield victory since 2016 and climb to fourth in the table.
"The players understood really well what to do in every moment," Amorim said. "We had to suffer a bit at the end, but it wouldn't be United without a bit of suffering.
"I have that feeling, I think it was a more complete performance than at Liverpool. You can say Liverpool did not deserve to win that game, though we deserved to win.
"Today we did everything. When it is like this I feel more complete as a manager. I like this win more than last week."
Amorim singled out Cunha, who scored his first goal for United, and Mbeumo for special praise as the pair continued to settle quickly at United.
"He (Cunha) feels more confident if the game is harder, I really like the way he defends today he was not jumping all the time," Amorim added.
"When he has the ball I have no concerns about his ability at all. He was struggling about not scoring goals, he can try to hide but everyone understood really well.
"He (Mbeumo) is a working machine, he is so good in transitions. The connection with Amad (Diallo), it is really hard because these guys are really fast, they are so good one-on-one."