Mills and Clark only managed ninth while the Kiwis won the race to claim gold and Clark says that they could have done more in the medal race.
"We just feel a bit gutted at the moment that we didn't put a good show on," Clark told BBC Sport. "We had the Kiwis on the start line and then we let them go to the right and we were wedged in with a few boats and couldn't follow them out there.
"Then when the wind dropped we knew the gold medal was gone from us.
"[However] Hannah's a legend. When we started sailing together 18 months we put everything in and we weren't even thinking about medals."
The medal was Britain's fourth silver in the sailing during the Games.