Michael Carrick's side led twice, through Harry Maguire and Patrick Dorgu.
But they were undone in defence as AC Milan scored three goals from close range before Ruben Loftus-Cheek raced clear to add a fourth and give former United manager Amorim a win against his old club.
This was only United's second defeat in a run of six preseason matches, which included a win over Atletico Madrid and a 1-1 draw with European champions Paris Saint-Germain.
"On the whole, (pre-season has) been very good, I think there are a lot of positives to take from it," Carrick told MUTV, United's in-house television station, in a post-match interview.
But the former United and England midfielder added: "We're disappointed with today. We didn't play well today, so there are reasons for that. In some ways, we need to learn from it, we need to improve, some of the boys playing some of their first minutes."
Saturday's match saw Marcus Rashford make his first United appearance since returning from a loan spell with LaLiga champions Barcelona.
United captain Bruno Fernandes missed a penalty for the second successive friendly, with Milan goalkeeper Lorenzo Torriani diving to his right to stop the shot after the Red Devils skipper had fired wide against Leeds in midweek.
Fernandes did at least provide the second-minute corner that was headed powerfully by Harry Maguire to give United the lead.
But Milan levelled after a defensive mix-up allowed Goncalo Ramos to break into the area and square for Samuel Chukwueze to roll home.
United were awarded their penalty just before half-time after Koni De Winter tugged back Youri Tielemans, but Torriani went the right way.
United regained the lead after Dorgu seized on a loose backpass from Filippo Terracciano, but Milan equalised again when Chukwueze's wayward shot was turned in by Alphadjo Cisse at the far post.
Rashford, frozen out by Amorim and loaned out to Premier League rivals Aston Villa before his temporary spell at Barcelona, came on as a substitute on the hour.
Milan went ahead in the 68th minute when Chukwueze's cross was headed home by Ramos, and three minutes later former Chelsea midfielder Loftus-Cheek sprinted through for Milan's fourth goal.
"A lot of the boys will be better for the minutes," said Carrick. "We've got a good squad, so there's decisions to be made."
Portuguese boss Amorim was sacked as United manager in January after 14 months in charge, with Carrick, now in charge full-time, leading the club to a creditable third-place finish in the Premier League after initially being brought in on a caretaker basis.
United begin the 2026/27 English top-flight season away to newly-promoted Hull on August 22nd.
