Vaughn Franklin told Associated Press (AP) a political message delivered by Rev Jasper Williams Jr at the service on Friday "caught the entire family off guard".
In an emotionally charged address, the Atlanta pastor described homes where fathers have left as "abortion after birth" and he hit out at violence within the US black community.
Responding to the criticism, Rev Williams Jr said: "I understand it.
"I regret it.
"But I'm sorry they feel that way."
Former President of the United States Bill Clinton, Stevie Wonder (pictured) and Rev Al Sharpton were among relatives, friends and supporters of Aretha Franklin who attended her funeral in Detroit on Friday.
She died at the age of 76 in August after being diagnosed with pancreatic cancer.
The service, held at the Greater Grace Temple, was already mired in controversy when a bishop leading the ceremony apologised for touching singer Ariana Grande.
Bishop Charles H Ellis III later told AP it would "never be my intention to touch any woman's breast" after he wrapped his arm around the 25 year old.
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