Arezzo council have asked Italy's soccer federation to investigate Juventus's 3-2 defeat by Spezia on Sunday which relegated their town's club from Serie B.
Juventus were drawing 2-2 before conceding an injury time goal which sent Arezzo down and gave Spezia the chance of staying up via a playoff.
"Arezzo council will ask the Italian soccer federation to speed up actions, in the immediate future, that can guarantee perfect regularity in a championship until the final day," it said in a statement.
Arezzo manager Antonio Conte, who played for Juve, has also expressed his anger at what he saw as a lacklustre performance from his former team.
Juve were promoted to Serie A this season after last year's demotion for their role in a match-fixing scandal.
Arezzo are awaiting a court verdict on whether the six-point deduction for their part in the scandal should be reduced, meaning they still have a chance of staying in the second tier.