Kate, 35, made the comments about Prince George and Prince Charlotte during a visit to Mitchell Brook Primary School in London to mark the beginning of Children's Mental Health Week.
Accompanied by her husband William, she addressed the children at the school about the importance of mental health support and compassion for others.
'People often ask me why I am so interested in the mental health of children and young people. The answer is quite simple: It is because I think that every child should have the best possible start in life,' she explained.
'When I was growing up I was very lucky. My family was the most important thing to me. They provided me with somewhere safe to grow and learn, and I know I was fortunate not to have been confronted by serious adversity at a young age.'
Speaking about her work with charity Place2Be, of which she is a patron, Kate added that she'd spoken to many children who keep their problems inside, and encouraged the children present to talk about their feelings, 'whether that is your mother or father, a teacher or a friend.'
'I know that in your school you have been working on a project to spread a little kindness and I think this is such an important thing to do,' she continued, referencing the work Place2Be had been doing within the school, including a Kindness Bench, where children can sit if they are feeling lonely or in need of support, and the Kindness Cup, which celebrates the good deeds of especially benevolent students.
'If you see someone who you think might need help, try and be kind to them. Keep a look out for them if they are on their own or seem sad or worried. Perhaps they just need a hug or someone to talk to. I know it is hard if you are feeling down yourself. But helping someone out will also make you feel so much better, too.'
'My parents taught me about the importance of qualities like kindness, respect and honesty, and I realise how central, values like these have been to me throughout my life. That is why William and I want to teach our little children, George and Charlotte, just how important these things are as they grow up. In my view, it is just as important as excelling at maths or sport.'
The visit came as Place2B released new key figures about the concerns of young school pupils, with their survey revealing that 68% of school children in London say that they 'worry all the time'.
The top concerns included their family (61%), friends being okay (50%), and their performance in school (49%).