The Red Devils crashed out of the FA Cup on Sunday following a penalty shootout defeat to Fulham at Old Trafford.
It's the latest setback for Amorim, whose side have struggled for consistency since he took charge in November after leaving his role at Sporting Lisbon.
In his 24 games in charge of the club, he has overseen nine defeats [excluding penalty loss to Fulham] from 24 matches in all competitions - winning just ten.
And should he suffer one more defeat from his next seven fixtures, he would hold the unwanted record as being the United manager to reach ten losses in the fewest games in the Premier League era.
That unwelcome honour currently belongs to Ole Gunnar Solskjaer, who hit ten defeats after 32 matches.
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With United languishing in 14th spot and on course to finish in their lowest Premier League position in history, they could endure a trophyless season for the first time since the 2021/22 term.
Having already overseen a Carabao Cup exit to Tottenham in December, Amorim's only chance of guiding United to silverware lies in the Europa League.
But they've been handed a tough last-16 draw against Spanish side Real Sociedad, while sandwiched in the middle of the two legs is a clash against historic rivals Arsenal.
And speaking on talkSPORT's FA Cup GameDay Live, ex-Newcastle boss Alan Pardew hinted that their next three fixtures could define not only this season, but next term too.
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Reacting to Amorim's post-match comments where he played down the importance of Europe's second-tier competition, Pardew said: "The Europa League is everything.
"It's everything for them, because otherwise the season is nothing.
"There will be no European football next year unless they win it of course.
"So it really is very, very important, and they've got Real Sociedad [away, Thursday evening], Arsenal at home [Sunday] and then Real Sociedad [March 13].
"Wow, what a three games they are!"
Chipping in, talkSPORT co-host Majestic then added: "And then after the international break, they've got [Nottingham] Forest away and [Manchester] City at home, there's no let up!"
Meanwhile United cult hero Lee Sharpe, who won ten trophies at the Theatre of Dreams, has stressed that Amorim must adapt his system to salvage any chance of success from this campaign.
Appearing on the talkSPORT Breakfast show, he remarked: "When you get into a football club and they're not used to playing the formation you want to play and they can't play at the top level in the positions that you want them to, then you have to adapt.
"He is being strong-minded, some say stubborn, but at the end of the day, you're sat 14th in the league.
"And to get results, sometimes you have to change your ideas and your plans."
Eight-cap England international Sharpe was then asked whether Amorim would be surprised by just how big the job at United is in trying to turn their fortunes around.
To which he said: "I would say so yes, I think part of the thing was that he didn't want to come at this stage of the season.
"He wanted to come at the end of the season so he could have a pre-season and do his own sort of transfer window.
"But yeah, I'm sure he's pretty surprised at the performances and him trying to get his message across.
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"You usually get a new manager bounce when managers come into clubs and he didn't really have one of those.
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"We've seen David Moyes have exactly that at Everton, so I think with the system he's trying to play and the players that he's got, I think he's probably been very surprised I would say.
"I think he would have thought he would come in and turn things around pretty quickly and it's not worked out that way."