The NSPCC in Scotland said it had witnessed an increase in the willingness of adults to share concern about children in the wake of the Jimmy Savile scandal and other high-profile sexual abuse cases.
It said social work departments were acting as little more than an emergency service following a surge of reports of abuse in the wake of revelations about the former Top of the Pops presenter.
Almost one-fifth of the 50,989 calls it received in 2012/13 about sexual abuse related to historic cases.
The figures were published in the NSPCC's annual report How Safe Are Our Children? The charity deals with all types of child harm including sexual and emotional abuse and neglect.
According to the research there were 3369 recorded sexual offences against under-18s in Scotland last year. This includes 285 cases of rape or attempted rape of children under the age of 16.
There were 1463 recorded offences of cruelty and neglect - down almost one-quarter since the 2009/10 peak of 1919 offences.
The number of children on a child protection register in Scotland between 2002 and 2012 increased by 34%, the report said. There were 2706 children registered at the end of July 2012.
The research highlighted the charity's concern over the rising trend of online abuse, citing an 87% increase in counselling sessions about cyber-bullying from 2011/12.
It says more than one in four children aged 11 to 16 with a social networking profile have experienced something "upsetting" on it in the last year.
The charity also said 132 children were referred to its Child Trafficking Advice Centre between November 2012 and October 2013.
Matt Forde, national head of service for NSPCC Scotland, said: "This report underlines the importance of the early help services, which might support families to stay on track and prevent problems escalating.
"We must make real the vision that child protection is the responsibility of us all: family members, neighbours, friends, and our whole public service infrastructure. It is teachers, nursery workers, police officers, doctors, nurses and all professionals who come into contact with children."
"Whilst the NSPCC can never afford, and will not attempt, to plug the gaps in government funding we are providing early and proactive support to families. Together with our partners in local authorities, through our local services and through our national helpline, ChildLine Schools Service and public information campaigns, we are learning what works in preventing abuse and neglect and stopping maltreatment from escalating."
Peter Wanless, chief executive of the NSPCC, said: "With record reporting of child abuse, hard-pressed children's social service departments have little choice but to raise the threshold of where they act.
"This is leaving large numbers of children with no statutory support. Acting alone, children's social services struggle to be more than an emergency service, getting involved when pain and suffering for children is already entrenched or risk is very high.
"Whilst poverty does not cause child abuse or neglect, it can put additional strain on families that are already struggling and tip them over the edge.
"Of course the NSPCC would support greater investment in direct support for children, but we also understand the fiscal climate. There has to be a better way for children.
"Social workers do an amazing and often thankless job under an intense spotlight but most are worked to exhaustion.
"We must stop seeing child protection as just the responsibility of children's social workers and realise that the real child protection system includes our whole public service