In moving to North America to continue his development at a higher level, Falkovsky played major junior with the Ottawa 67's of the Ontario Hockey League (OHL).

[3] Pushed down the depth chart, Falkovsky was rooted to the ECHL for the duration of the 2016–17 season, recording 21 goals in 54 games with the Adirondack Thunder.

[4] As an unsigned prospect of the Flames, on 1 July 2017, Falkovsky signed as a free agent to a three-year, entry-level contract with the Los Angeles Kings.

On March 8, 2019, Falkovsky left the Americans and was returned with the permission of the Minnesota Wild to former ECHL club, the Monarchs, at the trade deadline.

On 16 June 2021, Falkovsky was traded by Dinamo Minsk to SKA Saint Petersburg, in exchange for Lukas Bengtsson.