University tuition fees in England should be means-tested to allow students from poorer homes to pay less, an education charity has urged.
Two-thirds (65%) of 11 to 16-year-olds polled for the Sutton Trust voiced concerns about university costs.
While an average 17% said cost was crucial in deciding whether or not to do a degree, this rose to 23% among those from poorer families.
The government said it was improving information on student finance issues.
In total, 86% of 2,595 teenagers at state schools in England and Wales said they believed going to university was important in "helping people do well and get on in life", with 81% saying they were likely to go to university when they were older.
Of the teenagers polled for the Sutton Trust by Ipsos Mori, 67% said exam results were the most important factor when deciding whether to do a degree.
And 28% rated tuition fees as their biggest source of financial concern - for 19% it was the cost of student living, while 18% pinpointed not being able to earn while they were studying as the main problem.
Sir Peter Lampl, chairman of the Sutton Trust, said: "It is clear from this poll that many young people remain worried about the cost of higher education.
"Graduates face debts of over £40,000 with the higher fees and many will be paying for their university studies into their 50s.
"While there may have been some uplift in university applications this year, student numbers are not yet back to 2010 levels.
"We are urging the government to means-test university fees, as used to be the case, so that those from low- and middle-income families pay less for tuition."
A spokesman for the Department for Business, Innovation and Skills said changes meant the university system was fairer, more transparent and more progressive.
"No new student will pay fees upfront, there is more financial support for poorer families and loan repayments will be lower once graduates are in well-paid jobs.
"The rise in applicant numbers and the record number of applications from students from poorer backgrounds show that young people are not deterred by financial concerns.
"However, we recognise it is vital to spread understanding of student finance issues and that is why improving access to information is at the heart of our reforms."
Nicola Dandridge, chief executive of Universities UK, said: "There are still many misunderstandings surrounding student finance.
"It is vitally important that young people, and their parents, have access to good information about tuition fees and repayments when making their decisions about university.
"The most important fact to remember is that students or their parents will pay nothing upfront - tuition fees are covered by loans from the government. Students don't pay anything back until they graduate and are earning over £21,000."
The head of higher education for the University and College Union, Michael MacNeil, said: "We need our brightest young people aspiring to university and the courses best suited to their talents - worryingly the biggest barrier is the increased cost of a degree.
"Charging for education in a recession makes little sense, risks stopping many talented young people from fulfilling their dreams and robs us as a country of their full talents."
Students from England who started their degrees after September 2012 have been charged fees of up to £9,000 a year. However, these fees are not paid upfront.
Fees at Welsh universities also rose to up to £9,000 a year, but Welsh students at any UK university pay only the first £3,465 of their fees - the rest is paid by the Welsh government.
Scottish students taking degrees in Scotland (and EU applicants who wish to study in Scotland) do not have to pay for their own tuition.
Students from Northern Ireland who wish to study there, (and European Union students who wish to study in Northern Ireland) will pay course fees of up to £3,575.