United had a disappointing 1-1 draw at Ipswich on Sunday in Amorim's first game in charge since replacing the sacked Erik ten Hag, leaving them 12th in the Premier League table.
On Thursday they face Norwegian side Bodo/Glimt in the Europa League after one win and three draws in their opening four matches in the competition.
"It is said to me that it will be a special time," Amorim told his pre-match press conference on Wednesday. "I just want to win the game, just to give that happiness to the supporters.
"Before the match it will be like a new sensation but after the whistle it will be one more game and we want to win that match."
Amorim, who changed United's formation against Ipswich, said the club needed to feel "momentum".
"It's important when you are putting an idea," he said. "If you win it's a big help."
The former Sporting Lisbon boss admitted after the draw at the weekend that United would "suffer for a long time" as he puts his stamp on the club.
And on Wednesday he admitted he did not know how long it would take players to get used to his methods, explaining it was difficult to draw parallels with his previous experiences.
"You can say that this is a different league so it's harder than in Portugal," he said. "But I also have more experienced players and all these guys play for national teams.
"They just need to increase their confidence and at the moment I don't know how to answer that question. I don't know how long.
"But I will know that with a lot of games without time to train it will be tough for me but it will be tougher for them because they are on the pitch and they will suffer a little bit.
"I will try to help and we have to manage to win some games and try to increase that idea in the team."
Amorim said United had firepower in their ranks despite their lack of goals this season and that he would try to help out-of-form Marcus Rashford.
"We will try to find the right solution for him, as for the other players," he said.
"He has to be Marcus, first of all, to try to return to that moment. Then he will have the help of all the staff, all the club and all the fans because he's a Manchester United boy. But he has to be the first one to really want it."
