Coun Peter Box made the comment whilst speaking about a damning Ofsted letter which revealed serious failings in the council's services for youngsters in a meeting of the full council today.
Following remarks from Wakefield Conservative leader Coun Nadeem Ahmed that the improvement plan "must appropriately address the issues raised", Coun Box said: "Is the plan sufficiently robust? In my view, it is not.
"We need a more robust plan and the director [for children and young people] is aware of that."
The Ofsted letter, published last week after inspectors visited in February, said vulnerable children in the district were being put at risk of harm.
The education watchdog found youngsters were not being safeguarded appropriately due to “significant weaknesses” in council services and that social workers, with high case loads, did not have the capacity to meet the needs of children and families.
Coun Box said he accepted the letter in its entirety and it was clear the council need to improve its performance.
He said it was "disappointing" that a previous Ofsted inspection of children's services in 2016 had shown "more hopeful signs of improvement" and admitted the pace of change had been "too slow".
He told councillors he had asked chief executive Merran McRae to look at what immediate additional resources were needed to support a "robust improvement plan" and said the plan would be agreed at a cabinet meeting.
He said he had also asked Ms McRae to establish an improvement board and expected to see "clear impact" within three months.
The meeting took place a day after Coun Olivia Rowley was stripped of her post as the council's cabinet member for children and young people.
Coun Margaret Isherwood has replaced her, with Coun David Jones being appointed today as the chair of the Children, Young People and Skills Overview and Scrutiny Committee, Coun Isherwood's previous position.