The crew, which comprised 20 Syrians and one Lebanese, were rescued along with just 33 surviving animals.
The ship, named Queen Hind, overturned for unknown reasons on Sunday shortly after leaving the Romanian port of Midia.
Supported by the military, police, and divers, rescuers tried to right the Palau-flagged vessel and pull it to the port.
The losses from the incident are estimated to reach 3 million Romanian Lei (approximately £537,670).
The vessel was bound for Libya, with preliminary investigations suggesting it was overloaded, reported Romanian news site Digi24.
An urgent investigation has been called for by the country’s main livestock breeder and exporter association, Acebop.
Acebop president, Mary Pana, told AFP: “Our association is shocked by the disaster. If we cannot protect livestock during long-distance transports, we should outright ban them.”
Romania is the EU’s third-largest sheep breeder, after Britain and Spain, and a top exporter primarily to Middle Eastern markets. It is one of the bloc’s poorest members.
The country’s livestock transport vessels have been labelled “death ships” by activists as sheep risk being cooked alive during hot summer months on their long journeys.
EU health and food safety commissioner Vytenis Andriukaitis demanded Bucharest halt the export of 70,000 sheep to the Persian Gulf in July due to extreme temperatures.