The Social Services Inspectorate said the council's children's services were "serving some people well" but prospects for improvement were "uncertain".
The council's portfolio holder for health and community services, Howard Doe, accepted the criticism and said the council was recruiting more staff.
"Last year saw an unparalleled leap in demand as a result of the changes in police referral procedures and heightened concern for child protection following the Climbie Report," he said.
Inspectors commended the council's fostering and adoption department, its services for children in care and its family support services.
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