After a season with the Tier III South Shore Bruins, Dasklakis played his freshman season for the Terriers, playing just eight games, though that was in part because he had to leave midseason to play in the World Juniors. Daskalakis became a college hockey legend, being named an All-American in 1983-84 by the American Hockey Coaches Association and was a finalist the Hobey Baker Award that same year. He also led the Terriers to the prestigious Beanpot title in 1982
Shortly after graduating, Daskalakis signed a contract with the Bruins and started his pro career with their AHL affiliate, the Hershey Bears. Daskalakis spent the majority of his first pro season with the Bears, playing 30 games and posting an .864 save percentage while splitting time with Darren Jensen. However, he also played eight games in the majors that year, with a 1-2-1 record and an .830 save percentage. The next season, he would earn the full-time starter's job in the AHL on a team that featured a young Mike Vernon and played two more NHL games, losing both of them.
The next season, Daskalakis ceded his starting role to Doug Dadswell, who was at the time a rookie goalie out of college, similar to Daskalais himself. He played his last two NHL games and then saw his career take an unpleasant turn. In 1987-88, he played 26 total games for four different teams in the AHL and IHL. He closed out his career with a season in Europe as the starting goalie for Jokerit Helsinki, posting a 6.56 GAA.
Today, Daskalakis is the president of Celebrities for Charity, an organization he founded with fellow Bruin Ray Bourque. He is also the agent for Sergei Samsonov and retired NFL player Troy Brown.