What is the ruling on one who is ignorant of the application of the principle of "an eye for an eye and a tooth for a tooth" in Islam, believing it to be restricted to the law of our master Moses, peace be upon him, despite living among Muslims?

There is no sin upon one who is ignorant of the details of penal rulings, such as retaliation for gouging an eye or breaking a tooth. These rulings are communal obligations (fard kifaya). What is obligatory upon every Muslim, however, is to correct his faith and know what perfects his individual obligation (fard ayn) of rulings, such as prayer.