The Gunners' victory on Wednesday night came thanks to second-half goals from Jurrien Timber and William Saliba - courtesy of two corner routines.
Rashford started on the bench before entering the field of play in the 58th minute.
The 26-year-old touched the ball 22 times during his cameo but he failed to produce any shots or key passes.
United ended the game having registered just two shots on target - four less than Arsenal.
And their poor display, particularly Rashford's, was not lost on the Man United fans.
Read more on Man United
Amorim makes United history in first Old Trafford league game as Rashford overtakes Hazard
'Not a good thing' - Manc United fans' chant for Ruben Amorim makes him uncomfortable
A video has been shared on X where the United squad are clapping the away support.
Rashford can be seen walking away from the squad and down the tunnel. It's unclear whether his intentions were to snub the fans, but the United faithful have not taken it well.
One fan said: "Absolute state of Marcus Rashford here. Disgraceful. Should be an absolute priority to sell in the summer. Can't believe he still has so many fans. He couldn't care less about us."
"Rashford sulking as usual in the background," another said.
Most read in Football
Enzo Maresca questions Chelsea star's work ethic despite goal and assist during win
'They're a disgrace': Man United fan rips into Arsenal as Berbatov brands them 'new Stoke'
Carragher makes hilarious Salah U-turn as he celebrates goals wearing Man United shirt
Wolves fans viciously turn on Gary O'Neil in furious crowd footage at Everton
One stated: "I have always said he's a self-entitled player. No team spirit."
Another said: "If he survives this summer transfer, this club is rotten."
Former Man United captain Roy Keane, who was watching the game alongside Gary Neville, Jamie Carragher, and Ian Wright, shared the fans' feelings.
They were hosting a YouTube watch-along for The Overlap.
During the second half, Keane fumed: "I tell you what, Rashford has come on, his general play as a footballer is shocking."
Rashford also gave away the corner that led to Arsenal's second goal, and Neville later condemned United for conceding from a straightforward set-piece.
"That can't happen," said Neville. "It's a looped corner. You do scratch your head, you're there as a coach and spend hours going through these corners."
At full-time, Keane said: "United deserve that. One shot on target."
Arsenal's victory saw them cut the gap to Premier League leaders Liverpool, who dropped two points in a surprising 3-3 draw at Newcastle following a 90th-minute equaliser from Fabian Schar.
United's defeat, coupled with Newcastle getting a point, saw Ruben Amorim's side drop into the bottom half of the Premier League.
Last week newly-appointed Amorim revealed he is determined to get Rashford back to the strong form he enjoyed during the 2022/23 season.
During that time, Rashford scored 17 times in 35 league appearances, but Amorim said it will only happen if the English star heeds a two-word demand.
"I will try to help him," said the new United boss.
"That position is not the best one for him, especially in a game like that. We have to kick with high pressure, we have to kick the ball so many times and it was like fighting with two giants.
Manchester United fans rip into Marcus Rashford After Ruben Amorim's first game
"We'll try to find the right solution for him, as for the other players.
"But he has to be Marcus, first of all, to try to return to that moment and then he will have all the help of the staff, the club and the fans because he's a Manchester United boy.
Read More on talkSPORT
I couldn't stand arrogant Ibrahimovic and our fight forced him to leave club within days
Frank Warren thrilled as 'greatest boxing card ever' is confirmed featuring Daniel Dubois
"But he has to be the first one to want it."
Manchester United's next game is against Nottingham Forest on Saturday. Forest currently sit sixth on the Premier League table.