Children's untreated mental health issues could spiral into psychiatric problems later in life unless more is done in schools, say head teachers.
The National Association of Head Teachers says with a fifth of children having a mental health problem before age 11, it is a key concern.
A snapshot survey of 1,455 English heads suggests two-thirds of primary schools cannot deal with such issues.
The government says it has ring-fenced £1.4bn for children's mental health.
Russell Hobby, general secretary of the heads' union, NAHT, says: "We know the government is determined to improve children's mental health but there's still a danger that some children will take untreated mental problems into adulthood."
Mr Hobby said three-quarters of school leaders had reported that they lacked the resources needed to provide the kind of mental health care that children need.
"Although increasingly common inside secondary schools, almost two-thirds of primary school leaders say that it is difficult to access local mental health professionals," he said.
"Schools play a vital role in supporting children's mental health and building their resilience - but rising demand, growing complexity and tight budgets can get in the way of helping the children who need it most."
The chief executive of the mental health charity Place2Be, Catherine Roche, said children faced all sorts of challenges, such as coping with parental separation, the illness or death of a loved one, and dealing with substance abuse and domestic violence.
The vast majority of schools were already working hard to support children, she said, adding: "Teachers are not counsellors, and sometimes schools need professional support to make sure that problems in childhood do not spiral into bigger mental health problems later in life."
Place2Be and NAHT believe all schools need access to, or should host, professional mental health services, and the government says it wants all schools to make counselling services available to their pupils in time.
But the union's survey revealed that 64% of schools do not have access to a counsellor on site, and three-quarters of these said the most common barrier was financial.
"Although increasingly common in secondary schools, almost two-thirds of primary school leaders say that it is difficult to access local mental health professionals," Mr Hobby said.
"While we have a better acknowledgement of the extent of mental illness amongst children and young people than ever before, the services that schools, families and children rely on are under great pressure."
One head teacher who responded to the survey said: "We used to have a counselling service in school which was amazing, but due to budgetary pressures we had to stop this service. Now there is virtually no accessible provision in our area."
Another NAHT head said: "There is a big gap in provision in this area for primary age children. When we feel we need more specialist intervention or advice than we are able to provide, there is not much else to access."
The Department for Education said: "We're at a turning point in how we tackle children's mental health issues and are determined to get it right.
"That's why we're investing £1.4bn over this Parliament to transform mental health support for children and young people, and have also given £1.5m over the last three years to projects involving Place2Be."