Britain were edged out in the final by world champions Japan 53-51 despite leading at the interval at the Morningside Arena.
The victory completed a perfect tournament for Japan, who won all three of their matches in the round-robin phase to top the pool.
That included a 47-43 victory over Britain on Saturday.
Elsewhere on Sunday, France won the bronze medals by beating Canada 52-48.
This was also the same outcome as the round-robin match between the two countries, which the French won 50-46.