Manuel da Costa did not join the shooting section of Sporting Clube de Portugal until 1961, when he was already in his mid-30s, and had a relatively brief international sport shooting career. His most notable appearance during this time came at the 1964 Tokyo Olympics, where he placed 58th among 73 competitors in the small-bore rifle, prone, 50 metres tournament. This event was his specialty, and he won an Iberian Championship in this discipline during his Olympic year, as well as several other regional and national titles over the course of the 1960s. He had retired from active competition by the 1970s.