Kopat, who is one of the best Belarussian defensemen, is a regular player on the Belarussian National Team; he played 68 games for the national team through his career. He is however best known for the goal he scored in the 2002 Olympic Games' quarterfinals against Sweden. With 17:35 minutes played in a game tied 3-3, Kopat skated in the neutral zone and took a shot half-way between the red line and Sweden's blue line. The shot hit Tommy Salo's mask, bounced on his back then entered the net, a totally unexpected twist of fate for the Tre Kronor, who had been dominant throughout the whole tournament, unlike Belarus, who entered the tournament as an underdog. That win was most certainly one of the greatest moment in the history of ice hockey in that country.
Kopat was on the winning side of the 2006-07 Continental Cup and was named best defenceman of the Super Final.