The British crew needed to finish ahead of the Australian pair to have a chance of gold but the winners held their nerve and Bithell has praised the manner of their victory.
"We tried it," Bithell told BBC Sport. "We got the better of them at the start and managed to sneak ahead but we were kind of hoping the fleet would be there to hold them up.
"They sailed a fantastic race, we tried to attack them when we could but they held their nerve and they're worthy champions."
Team GB have four silvers and just the one gold medal at sailing so far at the Games.