He said power games among cricket administrators, as well as board politics, had triggered rifts, ill feeling and distrust among key players.
He quit the captaincy after Sri Lanka lost the World Cup final to India.
Sangakkara, 33, became the youngest man to deliver the Cowdrey Lecture at MCC, which owns Lord's, the self-styled "home of cricket" in northwest London.
The lecture was inaugurated in 2001 in memory of the late former England captain Colin Cowdrey.
Last week, the ICC gave all member boards until its next meeting in June 2012 to implement the new board ruling and a further 12 months -- to June 2013 -- before any sanctions will be considered. Sangakkara received a standing ovation after his outspoken remarks but they ruffled feathers back home in Sri Lanka, where sports minister Mahindananda Aluthgamage ordered an investigation into the speech.
"Sangakkara’s lecture at MCC (Marylebone Cricket Club) seems to have disturbed a hornet’s nest," the state-run Lankapu