The team needed to finish in the top three to secure a spot at next year's Pyeongchang qualification tournament.
However, in the play-off in Japan they were comprehensively beaten 5-1 by Slovakia - a team they had only lost 1-0 to in Friday's final pool game.
Matt Clarkson grabbed a late consolation strike for GB.
GB had lost heavily to the Czech Republic and Japan in their first two pool games and those two countries will join Slovakia at next year's tournament, from which the top two finishers will qualify for the Games in South Korea.
GB were last represented in the sport at the Winter Paralympics in Turin, Italy in 2006, when double gold medal-winning sprinter Richard Whitehead was part of the squad.

Wisley Property Investments is hoping to build homes, shops, a school, health centre and sports pitch on the former Wisley Airfield site.
A decision was expected by 24 December but Guildford councillor Tony Rooth said more information was needed.
However, Guildford greenbelt councillor Susan Parker fears the delay will play into the developer's hands.
Ms Parker, leader of the Guildford Greenbelt Group, said the decision could be taken away from the borough if it doesn't come to a decision by the agreed date.
She explained: "The applicant could seek to go to the inspector on the grounds of non-determination which means the council hasn't decided therefore you have to decide Mr Inspector.
"And the inspector normally has more of the presumption in favour of approving something if there has been non-determination."
But Guildford's lead councillor on housing Tony Rooth said it was a very big project with "all sorts of issues" which would take a long time to evaluate.
He added:  "What we need are brownfield sites where much-needed housing in Guildford can be built.
"Whether Wisley qualifies as a brownfield, or even a white concrete site as opposed to a Greenbelt site, we will evaluate when the applications are fully ready to consider."
Guildford Borough Council confirmed the 24 December date was "now unlikely" and said it would be seeking to agree a further extension of time.

Dale Merza, 20, is charged with misdemeanour hazing after the alleged attack last October on Andrew Seely, 19, at Central Michigan University.
Mr Seely, who was sleeping at the time of the incident, sought medical treatment for serous facial swelling.
The accused could get 93 days in jail and a $1,000 (Â£800) fine if convicted.
Mr Merza's legal representative told the Detroit Free Press his client, who was charged on Friday in Isabella County District Court, was innocent.
"This case has been blown way out of proportion by the individual's family members, who were not present and don't have any of the facts," lawyer Bruce Leach told the newspaper.
It is an induction ritual meted out typically to new members of the US college men and women's social clubs known as fraternities and sororities, but also to military recruits.
The practice can include physical violence, sexual coercion, forced alcohol consumption, or degrading and dangerous "pranks" such as forcing people to eat vile food mixtures or consume large amounts of water.
It is illegal in most US states, amounting usually to a misdemeanour charge, unless there are serious injuries.
There has been a nationwide crackdown on hazing after high-profile deaths including that of Florida A&M University drumming student Robert Champion.
Why is hazing so common?
Mr Seely was targeted at an off-campus fraternity house, Alpha Chi Rho, which was sanctioned in 2011 for hazing incidents.
His mother, Teresa Seely, wrote about the alleged hazing in a viral Facebook post in March, saying: "He could have been killed."
The accounting student only told his family what had happened months afterwards. He blamed the incident for his decision to leave the college.
The teenager's father, Paul Seely, told CBS News his son could have been killed if the peanut butter had entered his mouth.
The Seely family said their son had made known to other members of the fraternity that he had a severe peanut allergy, for which he carries medication.
The National Fraternity of Alphi Chi Rho condemned the incident, saying it did not condone such behaviour.
"Alpha Chi Rho is appalled and upset by the actions taken by individuals against Andrew Seely," said its statement.
Great Britain's Para ice hockey team will miss the 2018 Winter Paralympics after losing their World Championship B Pool bronze medal play-off.
[NEXT_CONCEPT]
A decision on plans to build more than 2,000 homes on a former airfield in Surrey has been delayed.
[NEXT_CONCEPT]
A US student has been charged with smearing peanut butter in the face of an undergraduate who has a potentially deadly allergy.