The England international believes that Amorim's job is complicated by the difference between his approach and that of Erik Ten Hag, who left the Old Trafford club earlier this season.
Speaking to Sky Sports, Maguire explained: "The thing is with the managers and the styles, it is not like they have come in and they have similar styles. They are the total opposite in terms of what they want and what they demand.
"So the transition period is going to be tough. We all have great belief in the manager and all his coaching staff. I am sure things are going to turn around. He knows exactly what he needs to do to get this club back.
"He has come in and done everything he needs to do. He is really demanding."
United's form has barely improved since Amorim's appointment. But Maguire has voiced his support for the United coach, describing him as a "winner".
Maguire, 31 - whose contract is due to expire at the end of the current season - said: "He is a winner, so I am sure he will be because he hates losing games.
"It is frustrating. We want to win football matches and make our fans happy because so far this season it has not been good enough."
Maguire also conceded that United have fallen well short of their own standards and expectations this season.
The veteran defender observed: "We can't really set a target at the moment because we are nowhere near good enough and nowhere near where we want to be in the league table.
"It is really disappointing what we have done until now. Everybody knows that. We know it is not good enough for this club."