As a youth, Nagy played in the 1993 Quebec International Pee-Wee Hockey Tournament with a team from Poprad. He began his career in 1995 as a junior by HC Košice in the Slovak Extraliga. He was drafted 177th overall in the 1997 NHL Entry Draft by the St. Louis Blues. After being drafted Nagy came to North America and played with the Halifax Mooseheads on the QMJHL for the 1998–99 season and was named the fans 7th most popular player during the 15 year celebrations.