The Portuguese coach achieved his first back-to-back wins since taking over in November, with last weekend's 2-1 triumph at Anfield lifting United to ninth in the league and providing a rare dose of optimism at Old Trafford.
But Amorim was quick to pour cold water on any excessive celebration, pointing out how fine the margins were in their victory over the reigning champions.
"We use the good spirit of winning games. We know that was a good weekend for us, but our focus is on the next game. That is in the past," Amorim told reporters ahead of Saturday's game at Old Trafford.
"We need to understand that football has changed a lot, especially in this kind of club. So we are not thinking about the last game. We are thinking that in this game, it is going to be really hard to win.
"If (Liverpool forward Cody) Gakpo shoots 20 centimetres differently, then the narrative would be completely different. So I just want to maintain some calm, some direction in what we are doing," he added.
Amorim acknowledged the pressure that comes with managing a club of United's stature, particularly when results do not go to plan.
"There is doubt if you are a manager in this kind of club. You don't win a lot of games, people are going to doubt you. They have reasons for that," he said.
"But my point of view is that we need to be clear on our path and not change so much. Because if we win one game, that's all."
Amorim faces a Brighton side one point behind United in 10th, and he was full of praise for counterpart Fabian Hurzeler, describing himself as a "huge fan" of the German manager.
"You can see by the way they play the game. Really intense, the quality is there, they believe a lot in what they are doing, even under pressure," Amorim said.
"It's going to be a very difficult game. Brighton is a team that's really fun to watch. They're really good on build-up, they are really strong, they are really strong on transitions in every aspect of the game.
"They are doing well in set-pieces this season. They are a team that is really complete, and we need to be really smart and to face that game with a real focus on everything that we do because they are a very strong team."
On the injury front, Amorim said Harry Maguire and Mason Mount were doubts after suffering knocks, which were "nothing serious," while Lisandro Martinez is close to a return to training as he recovers from a knee injury.
