Ibrahim Toure, who had been suffering with cancer, died aged 28 last week while his brothers Yaya and Kolo were on international duty with Ivory Coast at the World Cup.
Former Barcelona midfielder Yaya has, however, suggested that City did not grant him permission to visit Ibrahim shortly after the club sealed the Premier League title.
Instead, Manuel Pellegrini's side travelled to Abu Dhabi to face Al-Ain in a celebratory post-season friendly.
"He [Ibrahim] was my confidant, my best friend too. City did not want to give me a few days [before leaving for the World Cup with Ivory Coast]," Yaya said, as quoted by France Football.
"I went to celebrate the league title in Abu Dhabi, while my brother was dying in his bed.
"Afterwards, I was angry with myself for not having insisted. For not having enforced [my absence from the trip]. However, my [City] officials knew that I was suffering for a few months at seeing my brother's health decline."
Yaya had previously stated he would seek to clarify his future at the Etihad Stadium after the World Cup, following comments regarding his unhappiness from advisor Dimitri Seluk.