Arsenal capitalise on Bayindir error to beat Man Utd
Riccardo Calafiori scored the only goal at Old Trafford. The Italian defender pounced on a mistake by United's stand-in goalkeeper Altay Bayindir.
The Red Devils had 22 shots and enjoyed over 60 percent possession.
But an expensively-assembled new £200 million ($271 million) forward line of Matheus Cunha, Bryan Mbeumo and substitute Benjamin Sesko failed to find a way through against the Premier League's best defence for the past two seasons.
Only four other teams scored fewer than United's 44 goals in 38 Premier League games last season as the English giants endured their worst campaign for 51 years, finishing 15th in the table.
But Amorim insisted the performance showed tangible signs of progress, even if it was not reflected in the scoreline.
"We need to win games but that was completely different to last season," said the Portuguese coach.
"We were the better team. In the end we lose the game, but really proud of the performance.
"We proved today we can win any game in the Premier League, against a great team like Arsenal."
'Big result'
After finishing second for the past three seasons, the pressure is on Arsenal boss Mikel Arteta to deliver the club's first league title since 2004.
The Spaniard was left to depend on his reliable defence and goalkeeper David Raya to secure a huge three points as the visitors never got going as in attack.
"Big result," said Arteta. "First game of the season at Old Trafford when you feel they are building something."
He conceded his side will have to be much better if they are to rival Liverpool and Manchester City for the title.
"It certainly gives you momentum and confidence when you are not at your (top) standards.
"Today we weren't, to be fair. The team has to find that resilience through nine, 10 months of the season.
"We have to improve a lot of things and that will happen very soon."
The new arrivals have lifted the mood around Old Trafford and the majority of the 75,000 fans in attendance could at least leave encouraged by the display of Amorim's men.
Cunha and Mbeumo unsettled Arsenal's normally unflappable centre-back pairing of Gabriel Magalhaes and William Saliba early on.
United were undone by an error from Bayindir, deputising for the injured Andre Onana.
The Turkish international meekly flapped at an inswinging Declan Rice corner on 13 minutes, allowing Calafiori to head into an unguarded net.
Patrick Dorgu came closest to a United reply before half-time with a powerful effort from distance that hit the post.
Mbeumo and Cunha saw tame efforts easily saved by Raya, while the Spaniard did brilliantly to divert another Cunha shot across the goal.
Arsenal had held interest in Sesko for well over a year before instead pursuing Viktor Gyokeres as the solution at number nine.
The Swede had a quiet Premier League debut and was replaced before the hour by Kai Havertz.
Sesko made his entrance moments later, to a hero's welcome after rejecting the advances of Newcastle for the lure of the 20-time English champions.
United continued to enjoy the better of the play without finding the finish. Mbeumo's powerful header was expertly clawed out by Raya.
Arsenal held firm to keep up with Liverpool and City, who both scored four goals to win on the opening weekend of the campaign.