The report, which OFSTED has no plans to publish, shows that most parents are very supportive of their child's school. Where there was dissatisfaction no link was found to quality of education.
What does concern parents, it finds, is homework, assessment and the curriculum and - in secondary schools - behaviour.
Just last month the Department for Education and Employment issued draft guidelines on homework which said that modest amounts were "essential" to the drive to raise standards in literacy and numeracy.
The report is based on the confidental responses of a quarter of a million parents to the questionnaire which is sent out by OFSTED as part of the inspection process.
Parents are asked to respond to 11 statements about their child's school.These range from how it handles their complaints to the way it enables their child to achieve a good standard of work.
Schools are encouraged to collect the parents' responses in sealed envelopes to ensure they respond frankly and in private to inspectors.
According to the report, dissatisfaction with standards of achievement is uncommon and few parents feel their children do not like school. There was more concern generally among the parents of primary pupils than those with children at secondary school.
But said the report: "High levels of parental dissatisfaction are unrelated to school quality as judged by inspectors' grades." Case studies of 20 schools - both good and bad - confirmed the statistical finding that there was no direct link between parental dissatisfaction and quality. In fact, according to OFSTED, in some cases high-achieving schools were criticised more.
Chris Thatcher, vice-president of the National Association of Head Teachers, said: "Standards are a priority for parents but they are not in a high position.
"Parents are very much aware of the complex nature of what a school is about - it is not just satisfaction about performance in tests or academic achievement it is just as much about how their children are settled and happy.
"Most parents will tell you that the most important thing for them is that their children have to be, and are going to be, in an environment where they are relaxed."
During the past five years inspectors have observed 22 million lessons and since last September they have been identifying teachers - not by name - on the observation form.
Further unpublished research by OFSTED reveals that primary teachers are observed, on average, seven times during an inspection for a total of nearly four hours.
Secondary school teachers are observed by inspectors, on average, three times for a total of two-and-a-quarter hours.
Half of all primary lessons were observed for between 25 and 40 minutes and half of secondary lessons for between 30 and 55 minutes.
The findings are based on an analysis of 338,285 primary lessons and 93, 816 secondary lessons.