But Chris Humphries said schools do have a "critical role" to play in equipping young people with the basic skills needed for employment. And people who advise 14 to 16-year-olds on careers need to have better information about the jobs market.
Mr Humphries was addressing a Local Government Association conference in London on effective schools, on the day the task force met for the first time.
Mr Humphries, chief executive of the Training and Enterprise Councils' national council, outlined current skills shortages - mainly in computing, engineering and some areas of construction - and the impact they have at a national and a personal level.
But he stressed the broader skills sought by employers, and schools' key role in providing them via a broad educational foundation, flexible learning skills and - particularly - the encouragement of positive attitudes towards lifelong learning.
"If schools can address those issues - and I know you are fed up with people telling you what to do - then the task force can deal with the 95 per cent already in the workforce," he said.
"I am not trying to create another organisation that sits alongside Michael Barber's (standards and effectiveness unit). I don't expect the skills task force to say anything dramatic around key stages 1 to 3.
"But I think there is little being done around the issue of labour market information and dissemination, the advice and guidance side of key stage 4 and beyond."
The task force is expected to report within two years.