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.
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.
In 1987-88 Daskalakis split the season between four North American minor pro teams. He jumped to Jokerit Helsinki the next season and was the backup goalie for the American team at the 1989 World Championship. He retired at the end of that season.