Oxbridge should work harder to recruit state school pupils, a think tank says.
Cambridge says it seeks the brightest from any background
The Institute for Public Policy Research says the two universities should be more "proactive" in reaching youngsters with suitable grades.
Oxford and Cambridge have both reached agreement with the access regulator to increase their shares of students from a wider range of backgrounds.
They say they do make great efforts to encourage interest, but cannot take those who do not submit applications.
The institute's co-director Lisa Harker said: "Students getting three A grade A-levels at state schools are significantly under represented at both universities.
"Oxford and Cambridge must stop blaming a lack of applications for their failure to make progress.
"It does not matter how many bursaries they offer or how many students visit their campuses if students from non-traditional backgrounds are not applying."
Last week, England's Universities Secretary John Denham renewed his criticism that some institutions still "recruit the vast majority of students from a small minority of society".
These universities are "missing out on a huge waste of talent", he said.
A recent report from the Sutton Trust charity showed that just 100 schools, mostly in the independent sector, dominated entry to the best universities.
Oxford University takes 54% of students from state schools and its target is to reach 62% within five years.
Cambridge takes 57% of students from state schools, but has a target to reach between 60% and 63% by 2011.
The IPPR said that on current progress, Oxford would not meet its benchmark until 2016, while Cambridge would miss its by a year.
Oxford's director of admissions, Mike Nicholson, said: "Both Oxford and Cambridge are putting a lot of effort into trying to engage with students and make them more aware of the opportunities.
"But if they choose not to apply, that is the only certain guarantee that they are not going to get in.
"If students think they have the ability and the potential, then at least if they apply they will have an opportunity to demonstrate that."
Entry depends on interviews and in some subjects entrance tests as well as on A-level grades.
A spokeswoman for Cambridge University said it was committed to taking the brightest and the best students irrespective of their backgrounds.
But she said the IPPR report did not take into account the nature of A-levels. Not all are regarded as equal and some are not deemed suitable by the university as qualifications for undergraduate entry.