Ibrahim Toure died of the disease aged just 28 in Manchester last Thursday, while his brothers Yaya and Kolo were at the World Cup finals in Brazil.
"At the end of the season, I wanted to stay four or five days with my brother before flying to prepare the World Cup with Ivory Coast," Yaya Toure wrote in a column in France Football magazine.
"But City did not wish to grant me those few days. I went to celebrate the title in Abu Dhabi while my brother was dying in his bed.
"Fortunately, Kolo was at his bedside. Afterwards, I regretted that I had not insisted. However, [City] executives knew that I was suffering."
City had no comment to make in response to the remarks.