Universities Minister David Willetts said individuals with "good" grades were set to miss out despite an increase in the number of undergraduate places.
With less than a fortnight before A-level results are published, Mr Willetts suggested sixth-formers consider retaking exams or applying for apprenticeships.
More than 660,000 people had applied to start full-time undergraduate courses by the end of June – up nearly 12 per cent on last year's record-breaking figure.
Competition has been intensified by some 45,000 people reapplying after being rejected in 2009.
Experts believe the rise could leave some 170,000 would-be students disappointed.
Mr Willetts told the BBC yesterday that the Government had made an extra 10,000 places available this year.
But he added: "It is going to be tough. There are young people who sadly are not going to get a place, including perhaps some young people who really have got good A-level grades."