"Social bias" in some of Britain's leading universities has led to a "huge waste of talent and ability", said the universities secretary John Denham.
53.7% of Oxford students admitted in 2005-6 were from state schools
Although steps to widen participation had been taken, more needed to be done to boost the numbers of disadvantaged youngsters studying degrees, he said.
But universities could not offer places to students who did not apply, he told a vice-chancellors' conference.
So partnerships between universities and schools may have a key role.
Mr Denham told the meeting in Leicester: "No-one could seriously argue that the current social bias across higher education and in individual institutions - including some of the most sought after - reflects a system that reaches all of our most talented young people."
The government was removing the financial barriers to studying by providing more generous grants and bursaries, he said.
And much had been done to encourage universities to consider all the factors indicating a student's ability to succeed.
Participation had broadened and deepened with a steady increase in the numbers of students from low income families going to university, he said.
But he added: "Even the most talented must be sufficiently well prepared to study and succeed.
"So university partnerships with schools will become ever more important - to help schools deliver the high standards we want and to identify and nurture the young students of the future."
'Back to the cradle'
President of Universities UK Professor Rick Trainor said efforts to recruit more working class students were bearing fruit.
But he added: "There is a limit to what we can do, especially because social inequality and educational disadvantage go back to the cradle, and beyond.
"Universities can't, in and of ourselves, reverse the pattern of social inequality."
Both Oxford and Cambridge universities have targets to recruit about three quarters of their undergraduates from state schools, although they dispute the basis on which these are calculated.
But figures from the Higher Education Statistics Agency showed Oxford admitted 53.7% of its students from state schools in 2005-06, while the proportion at Cambridge was 57.9%.