The Blades slumped to another defeat that leaves them bottom of the Premier League table and with just one point from 10 games.
“We’ve got to really dig in, have a look in the mirror at ourselves individually, because it’s not good enough,” said Norwood.
Eddie Nketiah netted the opening three goals before a Fabio Vieira penalty – conceded by Norwood – and a first Arsenal strike for Takehiro Tomiyasu wrapped up a convincing 5-0 win.
The result takes the Gunners two points off the top of the table, with Mikel Arteta’s side unbeaten in their first 10 league games of the campaign.
“It is very disappointing,” Norwood said.
“We go in at half-time 1-0 down. Second half it’s difficult to really come and speak and say too much other than it’s not acceptable to keep losing the way that we are.
“It is easy to stand and say ‘we stick together through the hard times’, it’s easy to say that, but now we’ve got to show it."
This was a galling afternoon where – once United’s resolute defence was breached for the first goal just before the half-hour mark – the writing was on the wall.
The travelling fans sang the name of under pressure manager Paul Heckingbottom but they have still yet to see their team win on their return to the top-flight, with just one point on the board.
Nketiah’s touch and finish for the opening goal proved he can do the job as the England international set the Gunners on their way to a comfortable victory over the rock bottom Blades.
Wes Foderingham would have expected to be busier in the opening half but he was on hand to push a rasping Gabriel Martinelli strike wide of the post five minutes before the break.
The second goal arrived five minutes after the interval, Foderingham this time flapping at a Bukayo Saka corner with the ball dropping to Nketiah, who arrowed a shot into the top corner. A VAR check for a potential foul on the United goalkeeper failed to save the visitors.
Nketiah, who made his England debut of the bench in 1-0 friendly win over Australia earlier this month, saved the best for last.
Collecting a pass from Emile Smith Rowe, the 24-year-old rifled home from 20 yards to complete his hat-trick.
Nketiah initially picked up the ball to take a late penalty awarded after a lengthy VAR check by referee Tim Robinson after Vieira had been caught by Norwood.
But instead Vieira dusted himself down to send Foderingham the wrong way and further extend the lead.
Tomiyasu rounded off the scoring deep into added time after Mohamed Elneny’s flick on from a near-post corner was deflected into the path of the Japan defender.
Heckingbottom’s side are struggling with injuries – but he was not ready to use that as an excuse for a bad day at the office.
“Arsenal had a lot of the ball first half but Wes (Foderingham) had one save to make,” he said.
“Second half, the goals were really poor that we conceded and probably a reflection of how I thought the game was – they outfought us as well as outplayed us in the first half and that is what good teams can do.
“We are down to the bare bones and missing some big personalities and physicality.”