Club Atlético Vélez Sarsfield
Costa made his official debut against Unión La Calera in a 2–1 Primera División defeat at the Estadio Municipal Nicolás Chahuán Nazar on 12 February 2011, starting the match as right back and being replaced by Santiago Dittborn. On 3 March, he scored a vital long-range goal to help UC to a 4–3 away win against Club Atlético Vélez Sarsfield in the second stage of the Copa Libertadores, the club's first ever away win against an Argentine team in the competition.