While England makes such training available free to all adults, many of the courses in Welsh colleges, and from private training firms, come with fees attached.
Education and Learning Wales, the post-16 funding organisation, will now fund courses as part of a new Skills and Employment Action Plan - but the Welsh colleges' association, fforwm, said the "pivotal role" of the FE sector had not been acknowledged.
Colleges in Wales provide free basic skills training to some adults, such as those on benefit, but the Welsh Assembly sees universal entitlement as vital to tackling illiteracy and innumeracy.
Around a quarter of the Welsh adult population has problems with basic literacy and numeracy.
The plan was announced this week by the Welsh Assembly education minister, Jane Davidson.
She said: "Skills and employment are among the most powerful drivers of our economy, crucial to virtually everything we do.
"Building on the success of our first Skills and Employment Action Plan and working in partnership we have identified a new programme of action that will move us forward to achieve a high-skill, high-employment economy with all individuals fulfilling their potential."
Business training advisers will be used to help small companies to address the training requirements of their staff and a "workforce learning account" will be available to give employers access to the government-funded staff training of their choice.
Just under one in five Welsh adults of working age has no qualifications, the worst record in Britain. Lack of skills is seen by 7 per cent of employers as a problem affecting recruitment, compared with 5 per cent in England.
Fforwm says the report is lacking in detail, however.
A spokesman said: "We support the general framework which underpins the Skills and Employment Action Plan and recognise the very real economic necessity in mobilising the latent workforce.
"Schemes aimed at encouraging employers to improve the skills of their existing workforce and those aimed at helping more people into sustained employment need to acknowledge the pivotal role of the FE sector.
"The action plan has not made the roles and responsibilities to be played by individuals, organisations and sectors sufficiently explicit.
"Colleges already work very closely with local employers, tailoring training to meet their needs. Colleges are, however, very eager for the delivery of a credit and qualification framework that can help the sector increase responsiveness to industrial needs."