As the first anniversary of her graduation in eco-tourism and cultural history approaches, Linnea Borjars remains jobless and frustrated.

After finishing her studies at Sweden's Linkoping University, the 25-year-old accepted an unpaid, part-time position at Fair Travel, a non-profit group focused on human rights and tourism, hoping it would lead to a full-time job and a salary.

But no such luck.

When her contract ended in December, she declined the offer to stay on as an unpaid intern. Since then, dozens of applications and endless hours of networking have yielded just two interviews, despite a resume boasting a stellar academic record and a string of hard-to-obtain internships.

"I feel in some ways that I'm of no use anymore. It's like I'm posing nude in my cover letter, begging for approval, but I just keep on getting dumped," says Borjars, who lives a few train stops south of where young Swedes rioted last month, in part in an outcry against their miserable job prospects.

(Read more: Youth Unemployment Could 'Scar' an Entire Generation: ILO)

Borjars' situation is a reflection of the depth of the European economic crisis. It is not only unemployment but also underemployment — including workers who are overqualified, interns who are unpaid or low-paid and part-time employees who want full-time work — that has reached critical levels in many EU countries, and could leave a permanent financial and psychological mark on a generation.

The European Union's unemployment statistics do not account for university graduates who are employed to flip hamburgers, or part-time coffee shop baristas who want to work more hours.

But experts now argue that the number of people who are underemployed has become too great to ignore, and represents a huge loss of potential economic output.

Overqualified and Underemployed

To understand where underemployment fits in, it is worth looking at how the EU's statistics break down.

Last December, the most recent full figures available, 25 million of the EU's workforce of 240 million were unemployed and actively looking for jobs, producing an unemployment rate of 11 percent.

An additional 11 million were unemployed but had stopped looking or were not immediately available to start work, and were therefore not classified as unemployed. Adding them to the total would bump the jobless rate up to 15 percent.

Then there were more than 9 million part-time workers who wanted to work more hours but had no opportunity to do so — they were counted as employed but felt underemployed.

And finally there were those who were overqualified for their jobs and might well have been making more money elsewhere if they had found the right match for their skills.

There is no specific figure for the overqualified, but a study published in 2011 by the Organisation for Economic Cooperation and Development, a club of wealthy nations, estimated that they may number as many as 65 million in the European Union, or more than a quarter of the total workforce.

(Read more: Italy Youth Unemployment Hits Record 40.5%)

Daniel Feldman, a professor in management at the University of Georgia and a specialist in underemployment, puts the cost of unrealised economic output in larger EU member states from the under-use of skills in the tens of billions of euros.

While European politicians are focused on the deepening scourge of youth unemployment, which in countries such as Greece and Spain has topped 50 percent, they are also starkly aware of the threat from underemployment.

Getting people into their first job is one thing — and will be the focus of discussion among EU leaders at a summit in Brussels on June 27-28. But ensuring that those who have jobs are properly or fully employed, especially at a time when there are 2 million vacancies across Europe, is also critical.

Whether in the Netherlands, Belgium or Austria, which have a tradition of job-sharing, or in southern Europe and Scandinavia, where it is much less common, the number of people who work part-time, increasingly against their will, is soaring.

A fifth of the EU's workforce is now registered as part-time, up from 16 percent in a decade.

Lost Generation?

"The situation in Spain is terrible. In the Starbucks where I work, they look for people to work 10 hours per week," said Laura Higueras, 24, who studied chemistry at Universidad Autonoma in Madrid. "I have friends in Germany and Austria who work as engineers and chemists. In Spain, if you work at a Starbucks, you are lucky."

Martin Schulz, the president of the European Parliament, says Europe has not had such a well-educated generation since World War Two, especially in countries like Italy and Spain.

"Their parents invested a lot of money in the education of their children, everything they did was right," the German Socialist told Reuters in an interview earlier this year.

"And now that they are ready to work, society says: 'No place for you.' We are creating a lost generation."

David Blanchflower, an economics professor at Dartmouth College in the United States, who was previously a member of the Bank of England's monetary policy committee and studied unemployment figures in detail, reckons a fifth of the part-time workers in the European Union are underemployed.

(Read more: Millennials Looking Like the Next 'Greatest Generation')

In Britain, wage freezes, particularly in the public sector, have resulted in a decrease in the number of workers over 50 who choose to cut back on working hours. This hurts the young, who traditionally have picked up those hours.

"There is now a huge gap between these two groups. Before the crisis, they were equal," Blanchflower told Reuters.

"I argue that the young actually get a double whammy — they can't get jobs, but if they do, they can't get enough hours."

Studies have shown that part-time work often sets people back on the pay scale, rarely includes benefits and can hinder future career advancement. While working parents may be willing to accept that trade-off, the long-term cost for young people at the dawn of their careers can be high.

"If you have a large section of the job market that for a long time is dependent on short-term jobs, it can be very damaging to people's future prospects," said Dorothy Watson, a researcher at Dublin's Economic and Social Research Institute.

Poverty Trap

Bjorn Gustafsson, a professor in the department of social work at the University of Gothenburg, sees underemployment driving people into poverty and ultimately onto welfare.

"The process of becoming self-sufficient through employment is taking longer than it did before," he said. "They get low income, low living standards and end up in poverty, and they utilise other means of income, such as welfare and health benefits."

With more and more Europeans graduating from university, many companies are additionally demanding practical experience from job applicants. This has deepened the mismatch between theoretical college programs and the job market, and forced a growing number of young graduates to accept jobs they are academically overqualified for. Or else to study more.

In Stockholm, Linnea Borjars has filed an application for graduate school, but remains ambivalent about its usefulness.

"It's a dilemma — you rack up more college credits, but that doesn't necessarily make you more employable," she said.

While unemployment is a known cause of psychological and social problems, the mental effects of underemployment are less well researched. But experts say they are equally serious.

Feldman, who has written several books examining underemployment, lists cynicism, resentment, anxiety and depression as some of the common, long-lasting side effects.

(Read more: Children's Life Chances in Poverty-Stricken Europe Decrease)

"The effects are much longer-term than people think," he said. "Even after people get re-employed in better jobs, they still don't devote the same level of organisational commitment. They always keep looking over their shoulder for a better deal."

Goran Majlat, a 26-year-old from Croatia, returned to his home country in 2011 after earning a business degree at the University of Minnesota in the United States.

Even with overseas academic credentials, finding a job proved to be tough. Majlat went unemployed for seven months, adding to Croatia's 35 percent youth unemployment.

"I went through all seven stages of depression and couldn't get out of my house. You need money for everything — to drive, drink coffee and all that. It was terrible, " Majlat said.

He was eventually hired as a bell boy at a local hotel, but was let go after the summer. After another nine months without a job, he found a position as a sales representative and also works greeting holidaymakers at a yacht firm. The latter is "unglamorous but easy", he says.

"But you are lucky if you have a job — any job."