Amarnath's comments come at a time when India are struggling to save the home Test series against England and have lost 10 of their last 13 matches.
The 62-year-old said the selection committee, including himself, took a unanimous decision to sack Dhoni post the 0-4 loss in Test series Down Under and field a new captain for the following one-day series. But BCCI chief Srinivasan overruled it.
"It was a unanimous decision of all five selectors. The board president did not approve the decision to replace Mahendra Singh Dhoni," Amarnath told CNN-IBN.
"When you respect a person, you don't ask questions...but my question here is: you have a selection committee which thinks what is best for Indian cricket, then why it is not given a free hand?"
"We were trying to look ahead, we wanted a young captain to come in, specially in triangular one-day series so that we can go ahead and do something better in near future...If we don't look ahead, we won't have a good team in the future."
"We selected 17 players for the triangular series but we did not select the captain. The captain was selected by somebody else," said the former India cricketer.
Asked why the panel did not go against the board at that time, Amarnath said: "Yes, we did think about that, but the decision was not to resign at that time. We did not want to create a big stir there as the team was playing abroad and the series was going on."
The former India all-rounder's revelation did not go down well with the board while his contemporary Sunil Gavaskar called the move "incredibly courageous".
"I will not go into what he (Amarnath) has said. I don't think this has ever happened. I don't think it is appropriate to give statements like this," BCCI senior official Rajeev Shukla told reporters here.
"Whatever one has to say, one can say while participating in the selection meeting. Making comments about selection issues is not appropriate as it creates some kind of perception in the minds of players and fans."
"Selectors are independent. They are not under any pressure," Shukla added.
Gavaskar, on the other hand, told NDTV that if someone has the courage of conviction, he has to be admired.
"He (Amarnath) is prepared to face the consequences. It is a testimony of his self-belief. It needs to be admired. What Jimmy has spoken is incredibly courageous and, maybe, lessons need to be learnt from that," Gavaskar said.
Gavaskar said getting the team's approval from the BCCI president was an age-old protocol.
"It's a protocol, actually. Any team selected does go to the board for approval, not just the captain, even the 14 or 16 selected for a Test or for an overseas tour. That's the protocol not just in India, but I understand that is the protocol even in Australia and England. The final approval is up to the board, so I don't think it is out of the ordinary," he summed up.