The watchdog found 83% of children it questioned for a report on social media use lied about their age when registering with the likes of Facebook and Twitter.
This leaves them exposed to ads for alcohol, gambling, sex aids and other adult content.
The ASA said it will “not shy away from the regulatory challenges this report raises”, adding it will explore “whether we need to take a tighter line on age-restricted ads in social media”.
The ASA said 98% of the adult ads children saw after bypassing age-gating measures by using a fake date of birth did not target children and therefore adhered to the ASA Code of Practice.
But it warned the very fact that children were seeing ads for things such as alcohol, gambling and slimming aids was a problem.
Chief executive Guy Parker said: “On the face of it, our survey suggests that advertisers are sticking to the rules but children aren’t.
“But before we all lay the blame with parents and guardians, we need to be honest: if advertisers and social media companies know that children say they’re older than they are, don’t they have a crucial part to play too?
“We’ll be talking to them about self- declared age-gating and considering whether we need to take a tougher line. But we all need to be part of this conversation about how best to set the boundaries within which our children explore the world around them.”
He added that suppliers and retailers, along with social media companies, need to “address whether enough is being done to prevent children, by registering false details, from having age-restricted content”.
Parker said: “They need to ask themselves whether they really are doing all they can not to target children with ads for age-restricted products or services when they know a significant chunk of the child population is exposed to these ads.”