Da Costa played football at an amateur level in the French lower division. An intelligent midfielder, his career was plagued by injuries. Da Costa began coaching at
Rouen, and eventually became a professional coach when he promoted
Quevilly-Rouen to
Ligue 2 in 2017. Da Costa left Quevilly-Rouen in May 2020. A few days later, he was announced as manager of
SC Lyon. He was sacked from the job on 18 December 2020, after just one win in 16 games. On 15 March 2021, he was announced as manager of
Créteil. On 9 June 2022, it was announced that Da Costa had joined Ligue 2 side
Saint-Étienne as assistant manager to
Laurent Batlles. In June 2024, Da Costa became new manager of
Hesperange in
Luxembourg. ==Personal life==