But far from being disappointed, the 21-year-old from Carmarthen was ebullient.
"That bronze medal means everything to me after the team's [sprint] win on Monday, with the girls," she said. "It was so hard, but it was worth it."
She may be finding the Olympics "hard" but Finucane is definitely "living her best life," as she put it, even sleeping with her gold medal.
"I slept with it under the pillow, like a little tooth fairy," she said.
"I'll sleep with the bronze under my pillow as well. It's so surreal. That bronze feels like a gold."
Having won the women's team sprint alongside Katy Marchant and Sophie Capewell, Finucane's ambition to become the first British woman to win three gold medals in one Olympic Games, an achievement that would rank her alongside the past track cycling greats, Jason Kenny and Chris Hoy, is now beyond her.
Next up, though, are three days of individual sprint matches that climax with the race for gold on Sunday afternoon. "I've got nothing to lose," she said. "I've got two medals already, so I will leave everything on the track and see how it goes.
"I've got to make it there first.
These girls are really, really strong. I know I'm up there too, but I want to enjoy my Olympics."
Finucane, along with Marchant, progressed from their six-lap heats to the keirin semi-finals and then the six-rider final, but not without a scare for the Welsh athlete, after she narrowly scraped through her semifinal in a photo finish.
"I was like, 'I need to leave everything on the track for that final," Finucane said. "It was a really stacked field. To have [to race] six really strong women, I knew I had to dig deep."
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