During his stay of three and a half years the team won the Georgian league title three consecutive seasons.

Asatiani had been attacking midfielder in his early professional career at Torpedo Kutaisi before Lokomotiv Moscow's manager Yuri Syomin converted him into a ball-playing center-back due to his physique and the ability to recover possession and accurately pass the ball over long distances.

His passing, dribbling, technical skills and an eye for decisive goals made him a versatile and valuable player for both the club and the national team.

Despite his talent, he was unable to continue his career as a player past the age of 29 due to recurring injuries.

[1] In a 2024 interview, former long-term Lokomotiv Moscow manager Yuri Syomin named Asatiani one of the best defenders in the Russian Premier League during the 2000s as well as one of the most disciplined foreign players in Moscow-based clubs.