Juve announced after an emergency meeting on Tuesday (AEDT) that Agnelli, vice-president Pavel Nedved and managing director Maurizio Arrivabene have all quit their roles.
It comes amid an investigation into alleged tax fraud, which Juventus have denied, and on the back of the club registering a record loss of €254.3million for 2021-22.
Now, a statement from LaLiga has called the sport's European governing body to take action in response to the developments.
"Following the resignation of the Juventus board of directors, LaLiga demands immediate sports sanctions to be applied on the club," read a league statement.
"LaLiga filed an official complaint against Juventus with UEFA in April 2022 reporting financial fair play breaches being investigated by Italy´s Guardia di Finanza.
"Specifically, the complaint charges that Juventus accounted for transfers above fair value and under accounted for employee expenses, resulting in a breach of UEFA break even requirements.
"This Monday, in the same statement announcing the resignation of its board, Juventus acknowledges financial accounting irregularities, which are also aimed at misleading UEFA financial fair play authorities, among others.
"LaLiga continues to pursue these complaints against Juventus and demands immediate sporting sanctions to be applied on the club by the relevant authorities."
LaLiga president Javier Tebas has both overseen a strict level of financial discipline among the league's clubs, and has frequently been at odds with the state-owned model of Paris Saint-Germain and Manchester City.
In addition, he was one of Agnelli's most vocal critics, amid the attempts by Juventus and two of the teams under his watch, Barcelona and Real Madrid, to create the breakaway European Super League.
"LaLiga has long been a major proponent for the implementation, application, and enforcement of strong financial sustainability rules in football," the statement added.
"Financial sustainability is paramount to protecting the business of football. Protect our football."