He played for Boston University from 1980 to 1984. Daskalakis was named to the Eastern College Athletic Conference All-Star Second Team in 1982–83 and First Team in 1983–84. He was also named to the National Collegiate Athletic Association (East) All-American First Team, 1983–84. He played for the United States at the 1981 World Junior Ice Hockey Championships. In 1981 Daskalakis, undrafted by any NHL club, signed as a free agent with the Boston Bruins.He played 12 National Hockey League games for the Bruins between 1984 and 1987, winning three games, losing four and tying one.