After playing four seasons at the University of Massachusetts Amherst, he was signed to a professional contract by the Buffalo Sabres of the National Hockey League on March 25, 2008.

[2] On December 2, 2011, Kostka was traded by the Panthers, along with Evan Oberg, to the Tampa Bay Lightning for James Wright and Mike Vernace.

On July 19, 2013, Kostka signed as a free agent to a one-year, two way contract with the defending Stanley Cup champions, the Chicago Blackhawks.

After only nine games with the Blackhawks and approaching the last quarter of the season, on February 23, 2014, Kostka was claimed off waivers by the Tampa Bay Lightning.

[9] As a free agent in the off-season, Kostka opted to sign his first professional contract abroad in agreeing to a try-out with Swedish top tier club, Skellefteå AIK of the SHL on September 1, 2017.