Great Britain have missed out on the chance to qualify for the 2018 Winter Olympics.
Needing to beat Italy to progress to the final round of qualification, they lost 6-2 to the hosts in Cortina.
Italy top the pre-qualifiers group and go through to the qualifiers in September, with Great Britain second after wins over Netherlands and Serbia.
The British team, ranked 24th, have not qualified for the Olympics since 1948, when they finished fifth.
Italy, ranked 18th, were 4-0 up in the second period before goals from Ashley Tait and David Clarke got Britain back within two.
But the hosts re-established their four-goal lead in the final period to secure their place at the qualifying tournament in Norway.
GB head coach Pete Russell said: "We gave it our best shot and I am proud of them. But we have be better and we have to be more disciplined.
"We can take a lot from the tournament and it has given us plenty to work on ahead of April's World Championship in Croatia. We are a young side and I think we have a bright future."
Rene Fasel, president of the International Ice Hockey Federation, believes "politics" is holding Great Britain back.
"There is a huge potential in GB," he said. "I don't know why it doesn't work. Maybe we need people who have one goal. There are some politics there. There is a place for hockey. Ice hockey could be something we could bring but it is a headache.
"We should find an identity. The junior programme needs to be built up. Everyone has to move in the same direction.
"We are ready to help. We tried - but you are not easy people."