Amorim made his debut as United's head coach on Sunday when they drew 1-1 with Ipswich Town that to them 12th in the Premier League.
Marcus Rashford scored the first goal of their new era after just 81 seconds but a fourth draw of the season was the full-time result.
Many United players were unable to display their full capabilities and the team's overall performance led to even more dropped points.
Club legend Hargreaves watched on at Portman Road and revealed afterwards who he believes could be cast aside by Amorim.
"He [Amorim] was in front of me, and he was really frustrated, I'm not going to lie," he said via The Sun.
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"He wasn't happy with [Diogo] Dalot's positioning in the first half. [Joshua] Zirkzee's positioning in the second half made him a bit frustrated as well."
Hargreaves also added: "Many of these players won't be playing in three, four, or five weeks time."
Dalot was named in Amorim's starting XI for their trip to Ipswich, playing at left wing-back despite being a natural right-back.
He has started every Premier League fixture for United this season and already been left impressed with his new boss.
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"It's gone really well," Dalot said as per The Guardian. "He made an impact straight away in terms of his philosophy and the way he wants us to play.
"It suits the standards of the club, high-intensity football and working hard for the team. We have to give credit to him and his staff for all the information they gave us.
"It was really clear and obviously now we will take some more training sessions and games to put this into practice. He's really demanding. He's exactly what we need for this type of club.
"That's the standard the club should have, by demanding people are really professional and working hard for the team. That's the clear message that he gives us every day."
Zirkzee on the other hand has continued to struggle at United after his £36.5million summer move from Bologna.
The Dutchman scored the winning goal against Fulham on the opening weekend of the season but has failed to net another since.
His last six Premier League appearances have all come as a substitute, with goalscorer Rashford starting ahead of him against Ipswich.
Amorim will hope to help Zirkzee flourish under his management as he approaches a tough run of fixtures.
United next host FK Bodo/Glimt in the Europa League, a competition they have won just once in after four games.
League action then returns with the visit of Everton ahead of tough tests against Arsenal and Nottingham Forest.
Amorim's first Manchester derby comes away to Manchester City on December 15 before a Carabao Cup quarter-final clash at Tottenham.
The January transfer window will then offer the Portuguese a chance to bolster his squad, with some tweaks clearly needing to be made.