Born in Glew, Buenos Aires, Almirante Brown Partido, Acosta came through the youth system at Club Atlético Lanús, making his senior debut at the age of 18.

On 29 May 2008, aged 20, Acosta signed for La Liga team Sevilla FC on a five-year contract, for a reported fee of €7 million subject to a medical.

[4][5] On 4 February 2009, Acosta scored his first – and only – goal for Sevilla, in the first leg of the Copa del Rey semi-finals, a 2–1 home win against Athletic Bilbao[6] but an eventual 4–2 aggregate loss.

In July 2011 he was loaned to fellow league side Racing de Santander, joining compatriots Ariel Nahuelpan and Héctor Cúper (manager);[7][8] he started and netted on his official debut for the Cantabrians, but in a 4–3 away defeat to Valencia CF.

[3] After appearing in six out of seven games in the under-20s triumph in Canada, Acosta scored against Ivory Coast in a 2–1 group stage win in the Beijing Olympic tournament, en route to another international conquest.