In his letter to the Ministry, he has complained against being overlooked for the appointment to the top post, sources said.
Sinha has also told the government that if "justice" cannot be done to him, he should be given voluntary retirement, sources said here.
Admiral Robin Dhowan, Vice Chief of Naval Staff, was appointed as the Navy Chief yesterday superseding Sinha, who was the seniormost Vice Admiral.
Sinha lost the race for the top post apparently because majority of the 14 mishaps, including two major submarine accidents, took place under his command during the last 10 months.
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Joshi, who had 15 months left in service, resigned hours after the mishap involving submarine INS Sindhuratna in which two Navy officers were killed and several others injured. Earlier in August last year, submarine INS Sindhurakshak sank at the Naval Dockyard in Mumbai, killing 18 personnel on board.
Had he retired in August next year as per his tenure, Southern Naval Commander Vice Admiral Satish Soni would have become the next chief.
In the changed scenario, National Defence College Commandant Vice Admiral Sunil Lamba is expected to succeed Dhowan in May 2016.