The conference, run by the Demos think tank, focussed on how schools can best do this.
Mr Hunt defined the ability to bounce back as a particularly British trait. He believes today's young people need it more than ever at a time of increased global competition. He wants schools to help pupils develop the sort of "British spirit" that will help them perform, overcome adversity and flourish amid the pressures of working life.
"The great British spirit comes from our ability to overcome adversity and setbacks. Character, resilience and the ability to bounce back: it's what makes us British. As our young people face growing rivalry for jobs, high-status apprenticeships and the best university places, it becomes more and more important for schools to coach pupils about character. Because we learn best from the knockbacks that we receive, that is the message that schools must send to pupils. I want to see the great British spirit in all our classrooms," Mr Hunt said.
Demos is already running pilot projects to see how teaching character could work in practice, particularly among white working-class children.
Chief executive Claudia Wood said the pilots were investigating how extracurricular activities such as sport, social action and volunteering could transform pupils' self-esteem and self-reliance. "People might call it grit, resilience or skills for the 21st century, but there is a growing consensus from all parties that character matters, and that policymakers can help develop it from childhood," said Ms Wood.
Policy director Leora Cruddas said building character should permeate all subjects, wider school activities and school ethos rather than being "a bolt-on to the curriculum".