Senior players like Sachin Tendulkar, Saurav Ganguly and Virender Sehwag were heavily criticised after the team's first-round exit in the Caribbean with cricket-crazy Indians questioning their presence in the team.
"Sachin is hungry... Just be patient with Sachin, Sehwag and (see) what they are capable of," Shastri told a news conference on Sunday, a day before the team are to leave for Bangladesh.
"Show respect for what they have done. Guys, they have played for 15 years. Just be patient guys, give them some time and you will see what they are capable of."
India, who lost to Bangladesh in the opening match of the World Cup, play a three-match one-day
Tendulkar and Ganguly have been rested from the one-dayers but retained for the Tests. Sehwag made the one-day team but was dropped from the Test side.
"Please respect the guys for what they have done, they are not finished yet," said Shastri, who was given the role of cricket manager on an interim basis after Australian Greg Chappell resigned as coach following the World Cup.
Shastri, who also works as a television commentator, has asked the team to focus on enjoying the game.
"What I did not like in the last six months is the cricketers were going through the motions like they were doing a sort of a nine to five desk job," he said.
"If you don't enjoy what you are doing, forget about winning."