A convincing 7-2 win over Spain in their fifth and final Division 2, Group A fixture in Tallinn, initially put GB in contention for silver - Estonia having already secured gold and promotion the previous day.
A 7-1 win for Lithuania, however, saw them take second place meaning Koulikov's team required the hosts to beat Romania in the final game of the tournament to enusre they brought home bronze.
This they duly did with a 9-1 hammering of the Romanians, leaving Koulikov pleased for his players, while also leaving a feeling of 'what if'.
"Our ultimate aim was obviously gold but it did not turn out that way," said Koulikov. "We had some ups and downs in the tournament but the good times were very, very good indeed.
"We scored 30 goals in five games and at times were untouchable, but the defeat to Estonia cost us dear. I am pleased for the lads that they take a medal home with them and we can build on this for the future."
Jordan Buesa and Tyler Cooper both scored twice in the victory over Spain, while former Sheffield Steelers' forward cna captain Liam Kirk - drafted last summer in the NHL by Arizona Coyotes - took his points total for the tournament to 14 (5+9), making him forward of the tournament.
Forward Kieran Brown - joined in the line-up by his fellow Sheffield Steelers' apprentice Jordan Griffin - also enjoyed a positive week, finishing seventh in the overall scoring with two goals and five assists.