بسم الله الرحمن الرحيم
You did not sin rather you did a good job. The prevalent Fatiha is not proved and it is bida’h. It is mandatory to avoid participating in it. People should individually do isal-e-sawab for the deceased person by sadaqah, charity, tilawat and tasbihat etc.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.