Her success continued with a gold medal on the uneven bars and a 4th-place finish in the all-around at the 2002 Junior European Championships in Patras, Greece.

The Olympic year started strongly for Kozich, with a career-highlight victory in the all-around at the 2004 European Championships, where she narrowly defeated Daniela Șofronie of Romania.

She was the first Ukrainian to take this title since Lilia Podkopayeva in 1996, and joined a list of older compatriots such as Tatiana Gutsu and Ludmilla Tourischeva.

In late 2006, she began to regain the form that won her the 2004 European title, placing 13th in the all-around final at the 2006 World Championships in Aarhus, Denmark.

She became the official choreographer of the Japanese women's gymnastics team and was present as a coach at the 2010 World Championships in Rotterdam.