Williamson is competing at her sixth Games and was joined by three-time Olympian Naomi Folkard and rookie Amy Oliver at Lord's Cricket Ground.
They had high hopes of erasing the painful memories of Beijing, where they lost by two points in the bronze medal match, but fell to a 215-208 defeat to Russia.
To make matters worse, they were ahead throughout the match until Folkard fired down an uncharacteristic four, swinging the advantage towards Russia.
"You can't change it now, even if you'd like to," said Williamson. "We stuck to our process and our plan but it just didn't happen for us.
"However, I've learned from Beijing not to beat myself up too much.
"I'm sure I can sit down with my coach and he will tell me things that I should have done but it doesn't change what happened."
Williamson will take on Mongolia's Bishindee Urantungalag in the individual event, while Folkard will look for instant revenge against Russia's Kristina Timofeeva and Oliver faces highly-rated Indian Deepika Kumari.
"We started really strongly but we couldn't finish it off," said Folkard.
"My dodgy last arrow probably didn't help but I feel a bit better knowing that we wouldn't have won even if I'd shot a ten.
"It's a team event and everyone takes responsibility but it's still disappointing because you also want to do well for yourself."
Great Britain's men also crashed out at the first hurdle as they lost 223-212 on Saturday to Ukraine.