The claim is made by wellbeing charity Nurture UK, which commissioned research with more than 6,800 children in 25 primary schools in England.
Its report, Now You See Us, published today, claims that children's insecurities are often well hidden and need addressing, to prevent escalation into more complex mental health problems.
It acknowledges that schools do understand the link between attainment and wellbeing, and underlying social, emotional and mental health needs (SEMH).
Schools also want to support pupils, it claims, but systematic assessments are not being carried out to identify needs among pupils.
It says that more than 80 per cent of schools rely on "ad hoc identification" to pinpoint mental health difficulties, and only 15 per cent carried out universal screening of all pupils to identify those with particular issues.
"Under these circumstances, although pupils exhibiting severe SEMH needs may be identified by staff, children and young people who experience less overt difficulties or have sub-threshold needs may easily remain overlooked for prolonged periods of time," states the report.
"Without early intervention and support, those children are likely to see their SEMH issues escalate into more complex and embedded difficulties, increasing their risk of school exclusion, poor attainment and other negative outcomes."
It calls for increased early support and intervention to identify theses common SEMH needs before they escalate into more complex mental health difficulties.
For the study, pupils needs were measured using the Boxall Profile, an assessment tool developed by Nurture UK to help teachers tailor their approach to individual pupils.
The report describes the tool as playing "a major role in understanding what lies behind a pupil's behaviour as it provides teaching professionals with an accurate and precise understanding of their SEMH needs, as well as identifying the levels of skills they currently possess to access learning".
Emotional insecurity was among the top three SEMH needs: 29 per cent of children said they had difficulties trusting adults in school or asking for help when needed.
Other needs identified were problems paying attention (28 per cent) which meant children struggled to listen or take part in teacher-led activities.
Nearly a third (27 per cent) of child experienced difficulties sharing classroom equipment with other children or being polite towards others.
According to the report, teachers who took part in the study reported increased understanding of how their pupils' underlying needs were affecting their behaviour and said they adapted their practice to improve support.
For those schools that introduced support following assessment, there was a 23 per cent increase in the number of pupils with no apparent SEMH needs after five months, the report added.
The findings come just weeks after a review on school exclusions by former children's minister Edward Timpson called for schools to address underlying causes that might be affecting a child's behaviour.
The report recommends primary schools should use the Boxall Profile to obtain an accurate understanding of pupils' SEMH needs and Ofsted should take into account within inspections the extent to which schools have an accurate understanding of these needs.
Kevin Kibble, chief executive of nurtureuk said assessment tools such as the Boxall Profile would help teachers better understand pupils' underlying needs.
"We must help teachers identify and support children with SEMH needs before issues escalate, harming their education and potentially leading to exclusion," he said.