Great Britain, already qualified for next year’s European finals, lost their final group game, 89-80 to Bosnia- Hercegovina in Cazin.
Andy Betts hit 14 points and Nate Reinking added 13 as GB struggled after winning the first quarter 20-13.
Although they produced a late 14-3 run to trail just 85-80 with 20 seconds left, Bosnia closed out the win.
Luol Deng, who injured an ankle in the late stages of the win over the Czech Republic, was rested for the game.
Forward Joel Freeland had a rare start for Great Britain and responded with six first-quarter points as GB took the early initiative.
But Bosnia won the next two quarters by a combined score of 48-31 to leave GB with a lot to do.
Trailing by 10 points with 101 seconds remaining, two pairs of Flinder Boyd free throws helped shrink the deficit to 85-80.
But a winning end to Britain's triumphant summer eluded them as Nehad Dedovic and top scorer Kenan Bajramovic hit two free throws each in the last 20 seconds to seal a win that puts them into next year's last-chance additional qualifier.
Israel joined GB in next year's finals with a 98-61 thrashing of the Czechs in Tel-Aviv.
Defeat sent the Czechs to next year's relegation round as the bottom team in Group D and also forced France into the additional qualifier on points average.