Kurt Kursawe's side had taken the lead through Anna Sharkey, only for Malin Gustavsson to cancel out the advantage and force sudden death overtime.
And in the opening seconds Gustavsson scored again to leave the home side inconsolable.
“We wanted to finish at least top four in our group and we were top two so that was a big achievement," said Kursawe.
“I didn’t want it to finish here but we’ve come a long way. Now we are strong, we are good.
“Golden goal is hard, but these are the rules and you can’t change the rules. It was just a lucky shot in the end.
“I’m not happy about the loss but I’m happy about how we’ve stepped up. I’m proud of the girls.”
Less than six months ago Great Britain didn't even know if they'd compete at the Games with doubts about whether they team would be awarded a host nation quota place.
In the end, of all the team sports who secured their Games place as hosts, both at the Olympics and Paralympics, the women's goalball team have probably impressed the most, with a 5-0 win over European champions Denmark the tournament highlight.
Great Britain will have to qualify for the next Games in Rio but Jessica Luke believes the current team are likely to stay together and continue their rapid improvements.
"We just need practice and experience at the high pressure situations," she said
"I really hope we've encouraged more visually impaired people to get involved in our sport, to create competition for places and really build a future for our sport.
"We can't be too upset with what we've achieved. It's been a long journey and we proved we could perform credibly.
"It's been an incredible week and we've hopefully put the sport on the map and proved what we can do, especially as we beat the European champions 5-0.
"We definitely think we belong playing against these teams, we making them fight and we got two wins and a draw in the group stages to prove that."