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, Caudery managed to clear 4.70m - but she could not avoid catching the bar on her way back down in her last two attempts at 4.75m, despite appearing to have ample height.
Caudrey said she and other competitors struggled with the flow of the competition after the delay - but the Briton did not want to make excuses for her performance.
"I did clear the bar, which I was really happy with and I've never celebrated 4.70m so much, but I think it just threw me off my rhythm," she said.
"I'm not putting too much blame on myself. I'm not saying I couldn't have cleared that next bar because I think I had three good attempts," Caudery said.
"I feel a bit flat, to be honest, after that."
Caudery failed to qualify for the Olympic final last summer, despite entering Paris 2024 as one of the favourites after a breakthrough season in which she broke Holly Bradshaw's national record with a vault over 4.92m.
Eager to use that disappointment to fuel a pursuit of more major titles, Caudery made a promising start to 2025 by clearing 4.85m in February.
She took the decision to miss the European indoors two weeks ago to focus fully on her title defence here while she managed a minor calf injury, but will now fix her attention on a gold medal bid at the World Championships in Tokyo in September.
"It hasn't been a perfect indoors. It's disappointing to say the least but everything is a learning curve," said Caudery.
"I felt really good. I don't know what I could have gone on to jump without those technical difficulties, but there is no point thinking about that."
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