United are in a startling 15th place on the Premier League standings after their 12th defeat in 25 games and Amorin's eighth from 14 in charge.
The Red Devils had enough chances to score but failed to take them as Rasmus Hojlund had a shot cleared off the line, a couple were saved with Alejandro Garnacho curling just wide. The Argentine was also denied in a one-on-on situation by a brilliant save from Spurs goalkeeper Guglielmo Vicario with Joshua Zirkzee also being thwarted by the Italian shot-stopper.
The problems at the Old Trafford outfit are numerous - not only regarding performance but also with injuries and accusations of a "toxic culture" in the dressing-room. Among all the distractions, Amorim said his players need to show bravery and belief to tackle the issues head-on and not try to "run away" from them, saying that his belief in his side has not waned and wants his players to have the same faith.
"What you see guys and what you discuss every week, I also see. I have a lot of problems, my job is so, so hard here. But I stick with my beliefs," Amorim said in his post-match interview in north London.
"You grow and you learn a lot of things. We just need to face it and not run away, that is my feeling. Today will hurt, it is a tough pain to lose so many games, but then you can change things in a week."
Amorim faced a significant setback ahead of the match with the bad news that Amad Diallo, the one bright spot in United's season, would be sidelined for an extended period due to injury.
United's lineup at Tottenham lacked quality, with key figures like Kobbie Mainoo and Manuel Ugarte also missing from the midfield due to injury. To further complicate matters, the substitutes bench was dominated by youth, with eight players aged 19 or younger.
Among them, only Chido Obi was given a brief run out, replacing a fatigued Casemiro in the 90th minute.
"We have young kids, and we have to work with the young kids. We were not expecting so many injuries in one week. These things happen. Let's focus on the next game," Amorim commented.
While injuries, coupled with United's failure to bolster their squad during the January transfer window, can be viewed as factors contributing to Amorim's ongoing struggles, defender Matthijs de Ligt insisted that no excuses should be made.
"We still had a starting eleven with first-team players. It's no excuse. It's unfortunate to lose five players in one week, but that's part of football, part of life," de Ligt remarked.
"I believe you have to earn your luck. Right now, it seems we haven't earned it. I don't believe in luck coming out of nowhere."