Asta, a midfielder, played mostly at the amateur level in his early footballing years, also working as a bartender. During the 1994–95 season, played with Saronno, was his first one in a professional league (Serie C2). He then played for Monza of Serie C1; in 1997, Asta signed for Torino of Serie B, where he became a fan favourite, eventually becoming the team's captain during his time with the club; he helped his team to obtain a Serie A promotion in 1999. In January 2000, Asta was sent on loan to Napoli of Serie B, helping the club to gain promotion to Serie A; the following season, he led Torino to Serie A promotion, winning the Serie B title with the club.