Malinga announced his retirement last Friday, days after Sri Lanka Cricket questioned his participation in the lucrative Indian Premier League (IPL) after he withdrew from the upcoming England Tests citing issues with his fitness.
The paceman, who is in top form for the Mumbai Indians in the IPL, recently made himself unavailable for Sri Lanka's Test series in England, attracting criticism that he had chosen club over country.
Sangakkara said Malinga's decision was best for the team while Jayawardene said it was the right call from a personal point of view, according to the Cricinfo website.
"We were all well aware of the seriousness of his knee condition," Sangakkara said of the injury-prone bowler, who has pierced eyebrows, dyed blond locks and a distinctive slinging action.
"While I was captain we tried to manage him as carefully and sensitively as possible during the past couple of years," said Sangakkara, who quit as skipper this month following the team's defeat in the World Cup