Thakur stopped short of saying that action will be taken against Patil but said "right people in the BCCI" will speak to him soon over the issue which has created a major controversy.
Patil, a former international cricketer, recently disclosed that the selection panel would have dropped Sachin Tendulkar before he eventually quit international cricket and that it had also considered removing MS Dhoni from ODI captaincy ahead of the 2015 World Cup.
"Let me make it very clear. Sandeep, being a former chairman, should not have made these comments. When he was the chairman, he replied differently to the same questions. But after that [his tenure], it was different. It was totally unethical of him to do that," Thakur told PTI.
"One should refrain from making such unethical and unwanted comments in this area [selection matters]. It is because he has been trusted to become the chairman, because he has played enough cricket. There were four more selectors with him; they did not say anything. He should have avoided that," the BCCI president said.
Asked whether any action was being contemplated by the BCCI against Patil over the breach of confidentiality, he said, "The right people in the BCCI will speak to him soon."
Thakur went to the extent of saying such a breach of confidentiality would make it difficult for any of future employers of Patil to trust him.
"Any organisation, if they hire him, will think ten times that after leaving the organisation, he will speak about the organisation," Thakur said.
Patil's four-year tenure ended when the panel announced the 15-man squad for the ongoing Test series against New Zealand.