It did appear that the Portuguese would be suffering a third straight league defeat for the first time in his managerial career, with Josko Gvardiol's first-half header sending Man City ahead in the derby on Sunday afternoon.
However, Bruno Fernandes levelled the scores in the 88th minute, converting from the penalty spot, before Amad Diallo scored a sensational late winner for the 20-time English champions.
Amorim has now become just the second Man United head coach after Ferguson to win their first Manchester derby.
Amorim matches Ferguson feat in Manchester derby win
"Three points. We have a lot to do but massive for our fans. But I see the same game until 85 minutes. Maybe our conversation would be so different without the goals but the performance was the same. They were in the game for 90 minutes. We didn't control the result throughout but I think we deserved this. Good day for us," Amorim told Sky Sports News after the clash.
"You can feel it we were near to scoring. We improved our speed in our runs and had opportunities. We controlled the attack of City and we believed it in the end. We wanted it more when we scored the first goal. Congratulations to the lads.
"It's really important but when these game finished I remembered one week ago in the storm. We were 3-1 down at home to Nottingham [Forest] and I keep that feeling for these days to not get carried away. We needed it a lot the three points."
Amorim addresses Mount injury after derby setback
Amorim also discussed Mason Mount after the match, with the Englishman being forced off in the early stages of the contest.
However, the Portuguese has ruled out a potentially serious problem for Mount, claiming that the playmaker "stretched his leg".
The former Chelsea youngster will now be assessed before it is determined how long he will spend recovering from the issue.
"It's more the problem with Mason Mount, you think right away. We have a lot of games. We have to continue to win. This will change if we don't continue to win," said the manager.
"He [Mount] fits our style. He's a very good player inside and also outside the pitch. The type of character we want in this team and the club want. He made the movement and stretched his leg, he felt something. But we need him."
Man United will be looking to build on the morale-boosting win when they take on Tottenham Hotspur in the quarter-finals of the EFL Cup on Thursday night, before hosting Bournemouth in the Premier League next weekend.
Written by
Matt Law