Amorim, who took over from Erik ten Hag in November, endured a challenging introduction to the Premier League, guiding United to just seven league victories and overseeing their lowest top-flight finish - 15th - in over five decades.
However, Ugarte, who previously worked under Amorim at Sporting CP, has dismissed any doubts about the manager's position heading into his first full season in charge.
"We have to improve things, yes, but we're all very motivated," Ugarte said after United's 2-1 pre-season win over West Ham in New Jersey on Saturday. "We believe in the coach and in what he wants from us. That belief is very important."
Ugarte, 23, is entering his second campaign at United following his move from Paris Saint-Germain. His first season in England proved to be a mixed bag - marked by flashes of promise but also periods of struggle adapting to the Premier League's intensity. His dip in form late in the campaign saw him left out of the squad for the Europa League final defeat to Tottenham in Bilbao.
Amorim, though, has praised Ugarte's renewed confidence in pre-season, and the Uruguay international appears ready to shoulder greater responsibility in the heart of midfield.
"Last year was a period of change-new manager, new formation," said Ugarte. "This year I feel good, I'm excited. At a club like United, you need to perform and take on responsibility. I'm happy here, and I want to keep pushing forward."
With Amorim favouring a 3-4-3 setup, United are expected to reinforce their midfield options. The club has been linked with a move for a new holding midfielder to provide depth alongside Ugarte and veteran Casemiro.
Among those vying for minutes is 21-year-old Toby Collyer, who made 13 appearances last season. However, the young Englishman has hinted at a possible loan move in search of more regular first-team football.
"I want to play as many games as I can," said Collyer. "I'll sit down with the manager and the staff and decide the best path forward-whether that's staying or going out on loan. The goal is to start regularly for Manchester United, but I know I need minutes to get there."
As Amorim prepares for his first full campaign at the helm, much will depend on his ability to establish consistency, reinvigorate a misfiring squad, and continue building trust with key figures like Ugarte - one of his earliest supporters in the dressing room.
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