Is the word "Amin" part of Surat Al-Fatiha, or is it said for the acceptance of supplication?

What the questioner did is correct, for "Ameen" is a supplication meaning "O Allah, respond to us," and it is not a word from Al-Fatihah. It is recommended to say it after finishing the recitation of Al-Fatihah, based on the Prophet's (peace and blessings be upon him) saying: "And when he says: 'not of those who have incurred Your wrath, nor of those who are astray,' then say: 'Ameen,' Allah will respond to you." Narrated by Muslim. This indicates that it is not a verse from Al-Fatihah, in addition to the fact that it is not written in the Qur'anic manuscripts.