Ibrahim Toure passed away at the age of 28 last Friday, with reports suggesting he had been undergoing treatment for cancer.
Both Yaya and older brother Kolo are competing at the FIFA World Cup for Ivory Coast, and have decided to remain with the team, despite the passing of their sibling.
But, in a column for France Football, Toure alleged that City prevented him from being by Ibrahim's bedside following the conclusion of the Premier League season, instead insisting that he fly to Abu Dhabi with the team to celebrate winning the title.
City have refused to comment on the matter, although it is understood Toure did not submit a specific request for compassionate leave.
In the column, Toure wrote: "I confess that I am still very sad. I'm suffering because I feel I have done nothing useful for him the last few weeks.
"At the end of the season, I wanted to stay for four or five days with my brother before I flew to prepare for the World Cup with Ivory Coast, except that City did not want to give me a few days.
"I went to celebrate the league title in Abu Dhabi while my brother was in his sickbed. By fortune, Kolo was at his bedside.
"After that I blame myself for not insisting and for not leading them to respect me.
"However, club officials knew that I had been suffering for a few months seeing the health of my brother decline."
City have been known to grant compassionate leave on numerous occasions in the past.
In 2010, former striker Carlos Tevez was allowed time off to be with his prematurely born baby, and Emmanuel Adebayor was permitted to take leave after the Togo team bus came under gun fire at the Africa Cup of Nations.
Additionally, defender Pablo Zabaleta was given time away from the club after his father was involved in a car crash in 2011.