Mr Gove said state schools were producing school leavers with "the right values".
He made his comments after claims made by Richard Walden, headteacher at Castle House School in Newport, at the Independent Schools Association annual conference in Warwickshire earlier this week.
Mr Walden, chairman of the association, said state schools are failing to provide pupils with a "moral compass" because teachers are concentrating on delivering better academic results.
But Mr Gove said: "This is nonsense. State schools are getting better in every respect – from delivering a more rigorous education to ensuring children leave school with the right values.
"Only a few weeks ago, the head of the independent King's College School in Wimbledon admitted state schools are improving so fast they are increasingly becoming a threat to private schools.
"When I visit a school which gets great academic results it is always the case that everything else about the school is also brilliant – the sport, the community involvement, the best drama.
"Wasting talent, by telling millions of pupils that academic success is not for them, would be truly amoral."
Mr Walden said that too many state school staff are operating in "a climate of fear". He said fee-paying schools devote more time to extra-curricular activities and pupils were more likely to be able to tell right from wrong.
"Schools are turning out too many amoral children because teachers cannot find the time to teach the difference between right and wrong," he said.
A Department for Education spokesman said reforms would give schools more freedom.
He said: "All schools should provide a broad education and have a duty to promote the wellbeing of their pupils. Our reforms will reduce the number of tests that children take and have given teachers the freedom to use their professional judgement to tailor lessons.
"We are also giving all schools more freedom to offer extra-curricular activities that will build character. These include sports matches, debating competitions, cadet training and inspirational careers talks from outside visitors."