According to joint research by Kaspersky Lab and B2B International, 21 percent of users say they have lost either money or important information as a result of their children's online activity.
This number suggests that, in addition to the risk of children encountering cyberthreats, they can also cause inadvertent problems for their parents.
Kaspersky's research says that this percentile is not so surprising when you consider that 44 percent of respondents believe their children know little about computer technology - and 35 percent of kids know nothing of cyberthreats.
Delving into the figures also reveals that 12 percent of respondents said their children had accidentally deleted important information, while six percent faced unexpected bills from app stores after the youngsters got online.
All in all, says Kaspersky, every fifth polled parent confessed that they had had an experience of losing money or important data because of their children's actions.
Konstantin Ignatev, Web content analysts group manager with the company, said that, despite parents' first concern being to protect them from unwanted content on the Web, the problems that children may cause for their parents should not be forgotten.
"Applying parental controls is not showing distrust to your child; it's a sensible precaution with which you can, among other things, protect your device and the data on it. Interestingly, it also works the other way round: older children might use these types of software products to help their parents who know little about cyberthreats," he explained.
Kevin Gourley, lead volunteer with (ISC)²'s Safe and Secure Online scheme, said that the research shows that parents should be a lot more engaged with their children from a young age when it comes to online security - and they have to help them to be alert to the risks online.
"They need to be aware of their digital footprint and its consequences and that sharing sensitive information online can come back to haunt them and those around them," he said, adding that, generally speaking, his general rule that he teaches on the (ISC)² Safe and Secure Online programme is: If they can imagine a responsible adult standing behind them, and watching what they are doing on the Internet, and they would be happy with being watched by them, then what they are doing is ok.
"Using this mantra from an early age is a good way to help children pick up on what they should and shouldn't do," he explained.