On August 13, 1971, when Nagai was 19 years old, he debuted for Japan national team against Iceland.
[1] After retirement, Nagai became a coach for Furukawa Electric (later JEF United Ichihara) in 1988.
In 1996, he signed with Japan Football League (JFL) club Fukushima FC and managed in 1 season.
In 2006, he signed with his local women's league club Urawa Reds Ladies.
In 2012, Nagai was selected Japan Football Hall of Fame.