In his early years, Kostopoulos graduated from Fairwind Senior Public School in 1993. As a youth, he played in the 1993 Quebec International Pee-Wee Hockey Tournament with the Toronto Red Wings minor ice hockey team. After playing much of his minor hockey in the GTHL with the Toronto Marlboros and Mississauga Reps, Kostopoulos played one year with the Brampton Capitals of the OJHL (OHA). He was a 2nd round pick (18th overall) in the 1996 OHL Priority Selection by the London Knights.