Juve are under police investigation regarding "salary manoeuvres" of the financial years between 2019 and 2021 and, in April, the Spanish league filed an official complaint with UEFA regarding the Italians' alleged financial fair play breaches.
But, following developments on Monday at the Serie A club, who said the resignations were due to the "relevance of the pending legal and technical/accounting matters", La Liga wants action taken to "protect our football".
"As part of its campaign to promote financially sustainable football in Europe, La Liga continues to pursue these complaints against Juventus and demands immediate sporting sanctions to be applied on the club by the relevant authorities," said a statement.
"La Liga has long been a major proponent for the implementation, application, and enforcement of strong financial sustainability rules in football.
"The Spanish competition itself has applied its 'economic control' rules for nearly a decade, at the request of the clubs that make up the league.
"Financial sustainability is paramount to protecting the business of football."