The loss, United's third in five matches across all competitions, left the team 14th in the Premier League table.
Amorim, who has eight league wins since joining United in November, was asked if he should reconsider his tactics, but he refused to budge, stating that he would not change his approach unless he decided to do so.
"I understand that my record may not be what Manchester United fans expect," Amorim said. "However, I accept that there are many factors at play, and I am committed to my philosophy."
Amorim's team struggled to create chances and conceded several opportunities to City, who were led by Erling Haaland's two goals and Phil Foden's first start of the season.
Despite his resolve, Amorim's comments may have only added to the pressure on him, with chants of "You're getting sacked in the morning" echoing from the City fans.
Amorim's next test comes on Saturday, when Chelsea visits Old Trafford, and he will be expected to deliver a better performance and results to silence his critics.
Amorim's commitment to his approach is clear, but it remains to be seen if his team will be able to turn things around and start winning games consistently.
With no European football to distract from their domestic woes, United will need to regroup and refocus to avoid further losses and maintain their top-flight status.
The pressure is on Amorim to deliver results, but for now, he remains resolute in his approach, saying, "I will give everything, always thinking about what is best for the club."
Only time will tell if Amorim's resolve will be enough to turn United's season around.