The Duchess of Cambridge told of her "wonderful and secure childhood" as she spoke to headteachers about children's mental health.
Kate said it was the "duty" of parents and teachers to provide young people with safe and happy homes because not all children are as fortunate as her in their early lives.
Speaking at the Place2Be charity's conference for headteachers, she said: "I know that I was lucky. My parents and teachers provided me with a wonderful and secure childhood.
"But not all children are so lucky. Many children, even from stable and happy homes, are finding that their heads are too full."
She added: "It is our duty, as parents and as teachers, to give all children the space to build their emotional strength."
The Duchess, who wore a silver Matthew Williamson dress, was greeted to cheers as she arrived at the conference in London.
Kate was presented with flowers by Aaliah Beckford-Cordier, one of the children from the Crescent School.
Arriving after lunch, Kate struggled to keep her hair under control as gusts of wind swept the street.
The Duchess also spoke to Sam Gyimah, the MP for East Surrey who is Childcare and Education Minister, before going inside, where she spoke to a hall packed with hundreds of teachers.
She said: "I am sure you will agree that all children deserve time, attention and love from the adults in their lives. These basic qualities are so much more valuable than the always changing material and social concerns that can seem so important to young people."
The Duchess praised the teachers in attendance, saying: "Thank you for making Place2Be a part of your mission."
Finishing a rare public speaking appearance, Kate told the teachers: "I hope you know that your work is valued."
Lee Lewis, who is deputy head of a school in East London, called the Duchess's contribution an "inspirational opening speech".
Place2Be offers counselling in schools for young children.
Schools who have signed up pay a subscription in exchange for the visit of a trained counsellor who children can see without an appointment.
The Duchess is a keen supporter of work to alleviate children's mental health problems.
In February, she recorded a heartfelt video in which she lent her support to Place2Be's campaign to encourage children to seek help rather than stay quiet.
She said: "The stigma around metal health means that many children do not get the help that they so badly need. This needs to change.
"That is why the charity Place2Be is asking us all to talk openly this week.
"We need to help young people and their parents understand that it's not a sign of weakness to ask for help.
"A child's mental health is just as important as their physical health and deserves the same quality of support.
"No-one would feel embarrassed about seeking help for a child if they broke their arm and we really should be equally ready to support a child coping with emotional difficulties."
Speaking before the Duchess at the conference, Catherine Roche, the chief executive of Place2Be, said: "50% of adults with a mental health problem first experience it as a child.
"Just 6% of the annual mental health spend is on children. So early intervention is vital."