Great Britain won four of their five matches in Kiev
Great Britain agonisingly missed out on promotion from World Championships Division 1B despite a final-day 3-2 victory over Poland.
GB needed hosts Ukraine to beat Kazakhstan by no more than three goals but the game ended 2-2 in regulation time to see Kazakhstan claim gold.
Kazakhstan scored an overtime winner to leave Ukraine to settle for bronze.
Earlier, Jonathan Weaver, Russ Cowley and Ben O'Connor netted as GB won their fourth game of the tournament.
Filip Drzewiecki gave Poland the lead but two goals in 40 seconds from Weaver Cowley turned the game around.
Krystian Dziubinski levelled before O'Connor's scored a dramatic powerplay winner with seven minutes remaining.
GB head coach
“ To beat the four teams we have has been an amazing achievement”
Great Britain then endured an agonising wait during the final game of the tournament.
Ukraine came from a goal down to lead Kazakhstan 2-1 early in the third period.
With less than eight minutes remaining, GB looked set to claim gold and promotion to the elite top flight to face nations such as Canada, USA, Sweden and Czech Republic.
But Andrei Gavrilin's goal at 52:22 levelled the scores and once regulation time ended at 2-2, Kazakhstan's guaranteed point secured them gold.
Vitali Yeremeyev's overtime goal was the icing on the cake and Kazakhstan pipped GB to promotion.
GB had beaten Ukraine, Estonia, Lithuania and Poland in the tournament but ultimately their 2-1 defeat to Kazakhstan proved decisive.
Head coach Paul Thompson said: "This was the toughest World Championship group we have been in and to beat the four teams we have has been an amazing achievement.
"Tonight personified what we have been like all week. We were a team, a group together."