Efforts to involve parents in raising standards and tackling discipline founder because they are afraid of being "shown up" by teachers.
Mr Clarke admitted he had "no magic wand" to improve school-parent relations when he took part in one of Labour's Big Conversation consultations on ideas for the party's next election manifesto. He said it was necessary to create a culture of partnership between parents and teachers.
"The overwhelming majority of parents and teachers want to work together but don't quite know how," said Mr Clarke during the event at Gateway Community college in Tilbury, Thurrock.
He briefed Cabinet colleagues last week on the Government's major education priorities, which will be included in a five-year plan to be published in July. No details are available yet.
Parents, pupils, teachers and councillors were asked for views on issues ranging from 14-19 curriculum reform and discipline to the transition from primary to secondary school.
They rejected suggestions that Labour's next manifesto should include involving parents directly in teaching.
Johanna Allison, a parent governor, said: "It would frighten the life out of me. How can I teach my son when I do not have the skills? If I need to sort out a computer problem, correct my spelling or check some maths I ask him. Unless you are going to teach me, I cannot teach him."
Denise Cooper, a parent and Thurrock councillor, added: "There are a lot of parents of our age who did not have a happy experience at school. There is a fear that they are going to be shown up."
Respondents also argued against another major change in the curriculum saying more time was needed to examine the effects of previous reform.
Mr Clarke, who was absent for much of the two-hour discussion, rejected a call for a limit of 1,000 pupils per school, a measure intended to help pupils adapt to secondaries. But he said: "It can be destabilising when pupils from one primary go to eight or nine different secondary schools."
Calls for restrictions on pupils leaving school premises, after concerns were raised about children rampaging around town centres in their lunch break, were welcomed by Mr Clarke.
"There ought to be a presumption that pupils stay in school at lunchtime but that cannot be done just by locking the school gate," he said. A range of activities should be provided to keep pupils occupied, Mr Clarke added.
Discipline at Gateway college has improved dramatically since stricter lunchtime supervision and activities were introduced in September, according to Mike Morrall, headteacher.