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 today’s loss.
The defensive issues that plagued former manager Erik ten Hag have haunted Amorim as well, with both goals today coming largely thanks to blunders in the backline.
“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.