It marked swift revenge for the Poles who lost out on home ice in overtime to Paul Thompson's side last year in Torun when Sheffield Steelers' forward Ashley Tait struck a memorable winner.
It was GB who took the lead in the first period in Llubljana through Cardiff Devils' forward Phil Hill, after good build-up play by Russell Cowley and Mark Richardson enabled him to fire past netminder Krzysztof Zborowski at 17.13.
Poland came back in the second and drew level through Jaroslaw Rzeszutko at 37.57 and then went ahead in the 54th minute with what proved to be the game-winning goal when Mikolaj Lopuski found a way past Stephen Murphy in the GB goal.
Despite plenty of possession, GB couldn't turn their chances into goals, leaving them empty-haned after a campaign which had started promisingly last weekend despite the team being forced to endure a 26-hour coach trip to the former Yugoslav republic on Friday due to air travel problems caused by the Icelandic volcanic eruption
A 4-1 opening win against Division One, Group B whipping boys Croatia – gained after arriving at the ice rink only 90 minutes before face-off – was followed by a 2-1 win over Korea.
Thompson's players then produced a memorable performance to take favourites Slovenia into overtime on Tuesday night before going down 4-3.
A 2-0 defeat to Hungary the following day signalled the end of their gold medal hopes, leaving only the bronze available.
GB team manager Andy Buxton: "I think everybody will be disappointed that we didn't shoot as much as we should have done in the middle part of the game against Poland, although their goalie made some huge saves at important times.
"We won a bronze medal last year and we wanted to do it again. We don't want that to be a one-off.
"I'm proud of the players – it's been a very tiring week, particularly after the journey we had to take to get here. We'll have to go back and regroup and work out how we go a bit further next time."
Slovenia ended a two-year exile from the world's top-flight when their 4-1 victory over Hungary saw them clinch gold with an undefeated record.