He was associated with Salgaocar since 1979. Salgaocar has achieved a good deal of success under his guidance, having become the champion club of the country for two years in succession (1988 and 1989). Salgaocar, infact, made the Federation Cup final four times in a row (1987 to 1990) under him. Shanmugham has guided Salgaocar to success in the Rovers Cup,Sait Nagjee tournament,Naya Duniya tournament, Tamil Nadu Football Association Shield tournament and the Bandodkar Gold Trophy. They has also been the runner-up in the Rovers Cup, Sait Nagjee, Vizag Trophy and the Bordoloi Shield. Goa emerged the Joint winner of the Santosh trophy with Bengal in the 1983 Nationals at Calcutta and won it outright at the cost of Punjab in the 1984 championship held at Madras under his guidance.

Shanmugham was a member of the Indian team that won the Gold Medal in the first Asian Games, which were held in Delhi in 1951. He was also a member of the Indian team that participated in the Olympics in Helsinki in 1952. Shanmugham, who excelled as a centre-half played for Mysore from 1944 to 1954 and was the captain of the Mysore team that won the Santosh trophy in 1946 and 1952. He was the coach of the Karnataka team that won the national championship in 1967 and 1968. The government honoured him with the Bakshi Bahaddar Jivbadada Kerkar award in 1990.