The former captain has criticised his country's cricket authorities for being populated by "partisan cronies" in an hour-long speech for the Marylebone Cricket Club's annual Spirit of Cricket lecture.
The 33-year-old wicketkeeper-batsman urged Sri Lanka Cricket to stamp out corruption and infighting within the sport.
Sangakkara said Sri Lanka's shock 1996 World Cup win led to a change at the top of the sport in the country, bringing a loss of direction, transparency and accountability.
"The cricket board has been controlled and administered by a handful of well-meaning individuals either personally or by proxy rotated in and out depending on appointment or election," Sangakkara said at Lord's on Monday.
"Unfortunately, to consolidate and perpetuate their power they opened the door of the administration to partisan cronies that would lead to corruption and wanton waste of cricket board finances and resources."
Sri Lanka's sports minister last week said the entire national cricket board committee would have to step down after the country was left with a US$69 million (Dh253m) shortfall for jointly hosting this year's World Cup.
A divided board has been accused by commentators of severe financial mismanagement.
"It was and still is confusing," Sangakkara said. "Accusations of vote buying and rigging, player interference and even violence at the AGMs, including the brandishing of weapons ... have characterised cricket board elections for as long as I can remember."
He said the politics within the game would spill over into the team causing rift, ill feeling and distrust. "We have to aspire to better administration," Sangakkara said. "The administration needs to adopt the same values enshrined by the team over the years: integrity, transparency, commitment and discipline."
Sri Lanka go into today's game with a 2-1 lead in the five-match one-day series.