Randall, 23, and partner Olivia Federici returned a score of 89.170 points, 7.59 behind a bronze medal position.
The event was eventually won by Russian pair Natalia Ishchenko and Svetlana Romashina.
Randall and Federici were first British duet to reach an Olympic final in 20 years and they improved on their previous 14th place in Beijing four years ago.
Ascot-born Randall, 23 went to Hurst Lodge school and is a member of the Rushmoor Synchro Club along with 22-year-old Federici.
However, their Olympic Games are not over yet as the pair return to the pool on Thursday and Friday for the synchronised swimming team event.
Randall's younger sister, Asha, will also be involved in the team event.