In a competition disrupted by technical issues, Caudery - who has a season's best clearance of 4.85m - missed out on a medal on countback after failing to clear 4.75m.
The British record holder's second-time vault over 4.70m meant she finished behind silver and bronze medallists Tina Sutej and Angelica Moser, who both cleared that height at the first attempt, while France's MarieJulie Bonnin cleared 4.75m for gold.
"I'm really disappointed. I wanted to come out here after last year and do something and I know that I'm in shape to do something," Loughborough University graduate Caudery told BBC Sport.
"But that competition was really hard. There were a lot of issues and we were waiting for nearly an hour at one point."
The women's competition was delayed by around 40 minutes during Saturday's morning session because of an issue with the technology that lifts the bar.
Once it resumed, Cau...