He also floated an ambitious plan to make every school ensure that each child, whatever their ability, could rise two levels in achievement between each key-stage of the national curriculum for maths, reading and writing.
The existing system of national targets and league tables had raised standards but did not tell the full story because it failed to record the progress of individual pupils. It should be supplemented, not replaced, by measures showing how schools improved the prospects of the least able and most gifted children as well as the average pupil, he said.
He told a conference of new headteachers, in London, that he had an open mind on how this could be done and would publish a discussion document within two weeks.
"Despite everyone's efforts, lots of children are condemned to failure through no fault of their own," Mr Johnson said. "It is not the unavoidable destiny of these children to fail. Many are bright and talented enough to do really well but just lose interest or motivation along the way."
New incentives would remove the barriers that prevented disadvantaged children from realising their potential and getting the "extra push" they needed.
Mr Johnson said he had been impressed by schools he had seen recently in the US. A chain of schools in the Knowledge is Power programme had turned traditional admission systems "on their head" by reaching into the poorest ghettoes asking parents to send their most disadvantaged children to them. One such school in Washington had become the finest in the city with the best academic results; it was "pulsating with inspirational leadership, high expectations and a culture of achievement", he said. Middle-class parents were now desperately trying to get their children into the school.
Mr Johnson said he had invited leaders of the programme to visit England to see whether they could pass on lessons, particularly to independent trust schools. Such measures here "could revolutionise the prospects of disadvantaged children, making them the most exciting recruits for the most ambitious school".
Mr Johnson added: "If someone with the potential for eight grade A GCSEs only achieves five moderate passes, then that is not a success. But if someone who expected to achieve nothing gets their English and maths GCSE then we should recognise that achievement by the individual and the school."
His remarks come as schools are seen to be struggling even to meet broader national targets for achievements in maths and English. There are already "value-added" league tables taking into account schools' intake, but these are confusing and difficult to understand. A system for schools showing how many pupils met the individual targets set by teachers, as well as broader school outcomes such as the proportion of A* to C GCSE grades, might be clearer, he said.
There is also a political imperative to show how vast amounts of money spent since Labour came to power are improving standards not just generally but for particular groups, including boys and those from some ethnic communities with a history of poor educational achievement.
Ministers are desperate to overcome the "post-11 dip", where pupils' progress stalls for a couple of years. The 11-14 curriculum is already being reviewed in an effort to improve matters.
John Dunford, general secretary of the Association of School and College Leaders, said recognition that the present system had shortcomings was "long overdue". But the National Union of Teachers said league tables had to go. Steve Sinnott, the NUT's general secretary, said: "There is an increasing consensus that tests, targets and tables are undermining education and endangering the mental health of children."