Newcastle's Alexander Isak and Joelinton headed early goals to hand Amorim's team their fifth loss in their last six league games. They go into the new year 14th in the table, much closer to the relegation zone than the Champions League positions.
"I think (relegation) is a possibility and we have to be clear with our fans. We have to change something but this season will be really hard on everybody. It can make us stronger and we have to fight," Amorim said.
"It's also my fault in this moment, because I think the team is not improved, I think it is a little bit lost in this moment. So it's a little bit embarrassing to be much as United coach and to lose a lot of games. But we have to cope with that, difficult moments in the life of everybody. So it's a hard moment."
Amorim has had anything but a dream start to his United career, suffering five defeats in his first eight league games -- the worst record for a Manchester United manager in 103 years.
"Worrying times for Manchester United and Ruben Amorim," former United defender Gary Neville said on Sky Sports. "He came in as a young manager and knew it was going to be a big job, but it is far bigger than he could have ever imagined."
Neville called United "the worst pound for pound team in the country."
There have been questions over Amorim's commitment to his tactical 3-4-3 approach, and there were even more after Monday's loss. The defensive issues that plagued former manager Erik ten Hag have haunted Amorim as well, with both goals on Monday coming largely thanks to blunders in the back line.
"Of course, I didn't choose the players specifically for that position, but that I already knew," Amorim said, when asked if he has the talent to play his formation. "I have to sell my idea, if I'm going to change all the time it is going to be even worse.
"But I understand that they have a lot of difficulties, because they spend two years playing one way, and then they are playing another, and with a lot of losses, is really tough on them, and you can feel it during the game.
"I have to sell my idea. I don't have another one."
One of the game's ugliest moments came when Amorim took struggling Joshua Zirkzee off in the 33rd minute to boos from the Old Trafford crowd.
Ipswich claim first home Premier League win since 2002
Liam Delap and Omari Hutchinson scored either side of the break as Ipswich Town finally ended an almost 23-year wait to win a Premier League match at Portman Road with a 2-0 victory over Chelsea.
Not since April 2002, and a 1-0 win over Middlesbrough, have Ipswich celebrated home success in the top flight but on Monday hauled themselves one place up the standings to 18th with a tenacious triumph and handed Chelsea’s title hopes another blow.
Delap’s 12th minute penalty and a fine finish in the 53rd minute from former Chelsea product Hutchinson made for the perfect finish to an exciting year for the club, who were promoted at the end of last season.
Home hopes were raised early with the penalty award, as Leif Davis’ searching pass found Delap, who slid in to try and reach the ball and had his dangling leg caught by Chelsea goalkeeper Filip Jorgensen as he came rushing off his line.
It was Ipswich’s first penalty of the league season and Delap fired it underneath Jorgensen to the delight of the home crowd.
Soon thereafter followed a strong save from Jorgensen as Delap struck a firm effort across goal from a tight angle before Chelsea took control of the encounter and did almost everything but score.
Joao Felix had the ball in the back of the net after coming in at the back post with a 24th minute effort that was ruled offside after a lengthy VAR check.
Cole Palmer struck the woodwork twice, first with a quickly taken and curling freekick where the rebound fell to Christopher Nkunku, who hit it straight at Christian Walton.
The Ipswich keeper also denied Palmer with a sharp stop near the end of the first half.
But the expected equaliser never came, with Ipswich instead going 2-0 up early in the second half.
Hutchinson, who moved from Chelsea to Ipswich in a club record 20-million-pound ($25.10 million) deal before the season’s start, paid back some of his transfer fee with a smart finish for the second goal.
It came courtesy of an errant pass from Chelsea’s French international Axel Disasi, snatched up by Delap who was full of hard running throughout the match, often the lone man left upfront.
Delap checked as he ran into traffic before laying it off to Hutchinson, who needed to step inside before firing off the perfect finish.
"It's good to write history and finally get the first win at home," Hutchinson told television reporters.
Ipswich have let potential victories slip this season, so it was a tense atmosphere as the final whistle approached, before exuberant celebrations got underway.
"We've worked so hard this season and it's not gone right. The performances have deserved a win and today we showed we are excellent and we defended well, attacked them well. We're buzzing," said Delap.
