Ibrahim Toure, who had been suffering from cancer, died in Manchester last week at the age of 28.
After the news emerged, his brothers Yaya and Liverpool defender Kolo Toure decided to stay in Brazil, where they have been with the Ivory Coast squad at the World Cup.
But on www.francefootball.fr, Yaya Toure has been quoted as saying he had wanted to be with Ibrahim before joining up with the national team - and that he could not due to City's Barclays Premier League title celebrations.
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, although it is understood the club have always granted compassionate leave requests in the past.
Toure's agent Dimitry Seluk claimed in May there was a "big possibility" Toure could soon leave the club because he felt under-appreciated and disrespected by them, with a chief complaint being that his 31st birthday - which clashed with the Abu Dhabi trip - was insufficiently marked by the Blues.
Toure wrote on Twitter at the time of Seluk's comments: ''Everything dimitry said is true.
"He speaks for me. I will give an interview after world cup to explain."