The family is appealing the decision, saying in a letter to the NCAA that the athletic organization acted "hastily and without any regard for due process," the State College (Pa.) Centre Daily Times reported.
The family wants to meet with the Infractions Appeals Committee, the executive committee, the board of directors of Division 1 and possibly others.
The letter, sent Saturday by Paterno family attorney Wick Sollers, called the NCAA punishment of Penn State "unprecedented."
"This matter may be the most important disciplinary action in the history of the NCAA, and it has been handled in a fundamentally inappropriate and unprecedented manner," the letter addressed to NCAA President Mark Emmert charged.
"The Penn State sanctions are not subject to appeal," NCAA spokesman Bill Williams responded in a statement.
Sanctions include a $60 million fire, a four-year bowl game ban and cuts in the number of football scholarships.
The family disputes the finding of a report by former FBI director Louis Freeh which led to the sanctions. They charge the report reached incorrect conclusions that Paterno and others hid the child sexual abuse by former assistant football coach Jerry Sandusky.