Cocco made his professional debut playing for Unión de Santa Fe in the Argentine 2nd division in 1964.

San Lorenzo won the Metropolitano without losing a single game, making them the first unbeaten champions in the professional era of Argentine football.

In 1972 Cocco was part of the San Lorenzo team that won both of the Argentine league titles, this time they completed the Nacional championship without losing a game.

Cocco is one of only five players to have won four league championships with San Lorenzo, the others being Sergio Villar, Carlos Veglio, Roberto Telch and Agustín Irusta.

He made 12 appearances for the club, and joined the select band of players to have played for Boca Juniors and River Plate.