Captain Rohit Sharma, star batter Virat Kohli and allrounder Ravindra Jadeja retired from the shortest format after India won the Twenty20 World Cup last month.
The first T20 in the compacted series begins Saturday with the second on Sunday and the third on Tuesday. All of the matches are scheduled at Pallekele.
"Rohit Sharma and Virat Kohli are best players in the world. Looking at their talent and the kind of cricket they have played we all know where they belong, along with Jadeja," Jayasuriya said.
"Their absence will be loss to the Indian team and we have to take maximum advantage out of that."
Jayasuriya took over as interim coach after Chris Silverwood quit following Sri Lanka's first-round exit from the T20 World Cup.
Wanindu Hasaranga, who led Sri Lanka in the tournament, has been replaced as captain by Charith Asalanka.
Sri Lanka have called up Kusal Perera and Avishka Fernando, who were not part of the World Cup side, while also including uncapped allrounder Chamindu Wickramasinghe, who performed well in the Lanka Premier League tournament.
Sri Lanka's chief selector Upul Tharanga said fast bowler Dushmantha Chameera, originally named in the 16-member squad, has been ruled out of both the Twenty20 and the one-day international series against India because of an injury and his replacement will be named soon.
The three-match ODI series will be played on August 2, August 4 and August 7, all in Colombo.
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