United are seven points above the relegation zone, but are on the slide since Amorim took charge last month.
Alexander Isak and Joelinton struck inside the first 19 minutes as United lost a third consecutive home league game since 1979.
"That is really clear so we have to fight," said Amorim on United being dragged into a relegation battle.
"It is a really difficult moment, one of the more difficult moments in the history of Manchester United and we have to address it with honesty.
"We have to fight in the next game."
Worse could be to come as United travel to runaway Premier League leaders Liverpool on Sunday before facing Arsenal in the FA Cup third round.
Amorim has come under criticism for refusing to budge from his 3-4-3 formation since joining from Sporting Lisbon, where he won two Portuguese league titles.
The 39-year-old reacted to a disastrous start by replacing Joshua Zirkzee after just 33 minutes with Kobbie Mainoo.
United improved after the change, but the damage had already been done.
Amorim, though, was adamant that he will not change his ways, even if it ultimately costs him his job.
"You cannot go back, you have to continue to push," he added.
"We've had four training (sessions) all together, I was (brought) here because of my idea and I will continue with my idea until the end."
