Ibrahim Toure died last week in Manchester at the age of 28 after a battle with cancer.
Midfielder Yaya and Liverpool defender Kolo Toure are currently in Brazil with the Ivory Coast squad at the World Cup.
And Yaya Toure told France Football that City prevented him from leaving the title celebrations in Dubai.
He said: "City did not want to give me a few days. I went to celebrate in the wake of the league title in Abu Dhabi, while my brother was dying in his bed.
"In retrospect, I regret not having insisted. For not making them respect me. However, my employers knew that I was suffering for a few months seeing my brother's health decline."
Toure also said of Ibrahim: "He was my confidant, my best friend too."
City have declined to comment on Toure's remarks but it is understood they were not approached about the possibility of him returning to the UK. The club has granted compassionate leave in the past – former boss Roberto Mancini missed a game following the death of his father.
I'm obviously no great fan of City but they have a history of acting compassionately when it comes to personal bereavement. After the cake fiasco, I'm not really inclined to believe Toure.- icarus