The Payton Jordan Invitational meeting in California is renowned for always hosting top-quality 10,000m races for both men and women.
Pavey had hoped to achieve the qualifying mark in Ferrara so that she could map out her summer track season.
But like everyone else in the field in Italy bar winner Elvan Abeylegesse of Turkey, she fell short of the 31:40 target.
Ethiopian-born Abeylegesse won in 31:25.15, well clear of Ukrainian Tetyana Holovchenko and Nathalie De Vos of Belgium while fourth-placed Pavey had no excuses for her disappointing time.
"I suddenly felt bad but whether it had been a three or five kilometres race, it would have made no difference," she said.
"Even after two laps I didn't feel good, but I didn't want to drop out. But 32:21 is not good enough - I'll have to try again."