The warning comes from UK online centres, whose new research surveyed the internet attitudes of mums and dads from lower socio-economic groups.
The survey found that while three quarters of parents knew their kids were regular internet users, half of them didn't think their internet or IT skills were good enough to supervise or assist with surfing.
Around 60% of parents taking part in the survey said they worried about their children using the internet.
Topping the list of concerns were internet predators, inappropriate images and fraudsters, but other worries included cyber- bullying and the information children were sharing through social networking sites like Bebo and MySpace.
And it's not just internet safety that's causing concern. Around a third of parents also admitted to worrying about their lack of online know-how to help with homework and school projects on the internet.
Helen Milner, Managing Director of UK online centres said: "Technology has already changed how we live, work and socialise. Now it's changing how we bring up our children. Being a 21st Century parent increasingly requires new parenting skills - it's not just about looking after your children in the real world - you've got to look after them in the online world too. With more and more school services and homework activities involving the internet, cyber- bullying and internet predators hitting the headlines, it's not surprising that parents are anxious about their children being online.
"The real issue is that families already at a disadvantage are three times more likely to be offline, and that means poorer parents are also more likely to be the ones worrying about their kids on the internet, and about their own ability to help and supervise them."
The digital divide between online and offline families and the effect of new technologies on children's lives have become of increasing concern to Government, who over recent months have initiated the Byron Review into children's gaming and internet use, and a Home Access Taskforce to provide poorer families with a computer and internet connection. There is clear political appetite for tackling these issues, but Milner is concerned the focus remains too much on children and schools, and not enough on parents themselves.