2009-10: Sergei Kostenko skated for Kuznetsie Medvedie in Russia's MHL (U-22) and represented Russia in the 2009 Ivan Hlinka Memorial U18 tournament and the 2010 U18 World Junior Championship. He appeared in 19 games for Kuznetsie as a backup to starter Igor Glazkov and was 6-9-1 with a 3.41 goals against and .884 save percentage. Kostenko had mixed results in the Ivan Hlinka tournament. He stopped 33 of 40 shots in a 4-3 win over the United States. In the championship game against Canada he allowed six goals on 27 shots and was replaced to start the third in a 9-2 loss. Kostenko appeared in three games at the U18 WJC and was 2-0 with a 2.05 goals against and .902 save percentage. Russia finished fourth in the tournament after falling to Finland in the bronze medal game.
2010-11: Kostenko shared the goaltending duties with Alexander Plotnikov in his second MHL season with Kuznetskie Medvedi. He played in 28 games and was 6-18-2 with a 2.90 goals against and .898 save percentage. Kuznetsie finished 25th in the 29-team MHL.
2011-12: Kostenko appeared in 40 regular season games and started all seven playoff games for Kuznetski Medvedi in his third season. Kostenko was with the silver-medal winning Russian team at the 2012 U20 World Junior Championship but did not see any action and played for Russia in the 2011 CHL-Russia Subway Series. Kostenko was 15-11-8 for ninth-place Kuznetsie and had a 2.98 goals against and .897 save percentage. He started all seven playoff games and was 3-4 with one shootout loss with a 2.11 goals against and .918 save percentage. In his third year of draft eligibility, Kostenko was the tenth player taken by the Capitals in the 2012 NHL Draft when he was selected in the seventh round (203rd overall).