Nikola Milenkovic headed Forest into a second-minute lead before Rasmus Hojlund levelled in the 18th minute, but the visitors scored twice more through Morgan Gibbs-White and Chris Wood at the start of the second period, and Bruno Fernandes's effort in the 61st minute was no more than a consolation.
Gibbs-White's tame effort somehow beat Red Devils goalkeeper Andre Onana, before Wood looped a header into the far corner, with Lisandro Martinez, Matthijs de Ligt and the home side's stopper all culpable.
The defeat has left Man United down in 13th spot in the Premier League table, eight points behind fourth-placed Manchester City ahead of next weekend's Manchester derby.
Amorim rues mistakes in home loss to Forest
"Tough game. We started really bad, the first play we suffered a goal and then it's hard to try to fight. We then controlled the game and had a lot of situations," he told BBC Sport.
"We improved the movement in the last third. We managed to draw the game and then at half-time we were ready to go for the win and then started really bad. Two goals. Then we tried a lot of things with not a lot of quality.
"We didn't have many situations to score. Tough game in a tough moment but we have to continue the job. This is a long journey. We are improving in some aspects. We have to win games to help us improve the team.
"We are in the start of something so big that we pay attention to every detail. We already know it's a big job so we have to continue."
Amorim addresses substitutions with Fernandes surprisingly replaced
Amorim also revealed that he had to replace Fernandes late on due to the captain's 'tiredness', while he also explained his thinking behind his other substitutions at Old Trafford.
"Bruno [Fernandes] was too tired and I wanted [Mason] Mount to play that position of second midfielder who opens a bit on the left," the head coach told Sky Sports News. "Josh [Zirkzee] plays with Rasmus [Hojlund] to have combinations, [Leny] Yoro goes off because we can't give him too many minutes.
"We put Harry Maguire on because of set-pieces, to control more who was winning all the first balls, the only way to attack Nottingham was transitions, to try and win first and second balls. When Harry was on the pitch he won all the first balls.
"It's not a surprise [the start] because we come in the middle of a lot of games. It's really disappointing for the fans, after so many times with disappointment, but we are here to do a job and will continue doing the same things to improve the team."
Man United will be bidding to bounce back from their latest setback when they tackle Viktoria Plzen in the Europa League on Thursday night, with that clash coming three days before the Manchester derby.
Written by
Matt Law