Shastri also said the fans should give the seniors some time to see for themselves what they were capable of.
"Sachin (Tendulkar) is hungry for runs. Just be patient with Sachin and Virender Sehwag and see what they are capable of," he told a news conference on the eve of the team's departure to Bangladesh, where they will play three one-dayers and two Tests.
The performance of the senior players came under scrutiny after India bowed out of the World Cup in the first round, but the national selectors persisted with them while announcing the squad for the Bangladesh tour.
While Tendulkar and Sourav Ganguly were dropped from the one-day side for the upcoming Bangladesh tour, they were picked for the Tests. Virender Sehwag was retained only in the one-day side.
Shastri said the seniors deserved respect from the fans.
"Show respect for what they have done. They have played for 15 years. Just be patient, give them some time and you will see what they are capable of.
"Please respect the guys for what they have done, they are not finished yet," Shastri pleaded.
Shastri, appointed on an interim basis after Australian Greg Chappell quit as coach last month, said he had been advising the players to enjoy their game.
"What I did not like in the last six months was that the cricketers were going through the motions like they were doing a sort of a nine-to-five desk job.
"If you don't enjoy what you are doing, forget about winning."
Shastri, a former Indian captain, also said the players had left behind the World Cup disappointment and were focused on the Bangladesh tour.
"We have left behind what happened at the World Cup. The players are now raring to give their best."