Federico Allende, a defender for lower-division club Sport Pacifico, bragged in a radio interview about using the needle several times against strikers from top-division club Estudiantes.
Allende said that players had to be clever in order to win.
Pacifico's president Hector Moncada vowed to expel the player.
"We are devastated. This incident has tarnished the team's good work. I will expel him from the club," Mr Moncada told Clarín newspaper.
Pacifico won the match 3-2, knocking Estudiantes out of the competition in a major upset.
The players were received like heroes in the small western town of General Alvear when they returned from Buenos Aires, where the match was played.
But the good atmosphere soon turned into bad news.
Allende gave Cordoba's Vorterix Radio an interview on Tuesday in which he said "you need to play dirty" to beat big clubs like Estudiantes de La Plata.
"I kept piercing the Estudiantes strikers with a needle," said the Pacifico defender