Companies struggling to hire and retain millennials may be looking for talent in all the wrong places.

That’s according to results from a new survey in which 1,200 c-suite executives, human-resources officers, and people aged 18 to 26 were asked how they viewed the entry-level job market.

Some 70% of the employers told surveyors from the Rockefeller Foundation and Edelman Intelligence, a division of the public-relations firm, that they screen entry-level applicants’ resumes for bachelor’s degrees. Meantime, 40% of companies complained that high employee turnover is the result of workers feeling overqualified for their beginning roles. Most of the recent college grads confirmed that their jobs tapped skills they picked up outside of school.

“I’ve heard of employers requiring college experience and months of recent work experience for jobs at a call center. Twenty years ago that wouldn’t have been the case,” said Abigail Carlton, a managing director at the Rockefeller Foundation. Only a third of Americans aged 25 to 34 have graduated from college, but a university degree has become a “blunt proxy” for ability, she said, leaving behind many young people who are capable of learning on the job.

Employers rely on college degrees because they often signal applicants possess so-called soft skills, like dedication or resilience—attributes that can be harder for employers to measure than technical skills, said Matt Sigelman, chief executive of Burning Glass Technology, a labor-market analysis firm.

“It’s clear that many people are paying a significant price because companies don’t use more efficient mechanisms,” such as personality tests, to identify those qualities in job-seekers, Mr. Sigelman said.

The mismatch between employer requirements and the underlying skills entry-level roles demand could be exacerbating labor shortages, Ms. Carlton said, especially considering that young people without a degree reported feeling less comfortable job-hopping.

While the U.S. unemployment rate hovers near a historic low under 5%, joblessness among those between 25 and 34 is slightly higher, and nearly twice as high for people under 24, according to the Bureau of Labor Statistics.

The disconnect between job requirements and applicants’ skills is even more pronounced in regions of the country with large concentrations of college graduates. Matthew Bidwell, a management researcher at the University of Pennsylvania’s Wharton School, says employers may be “up-credentialing” job requirements in places like large metropolitan areas and university towns to control the number of applicants.

A January report by economists at the Federal Reserve Banks of Philadelphia and Atlanta found that employers’ education preferences often vary by region for the same job. Job listings for online customer support staffers in Atlanta were 22% more likely to ask applicants for bachelor’s degrees than postings in Charleston, South Carolina, according to the research.