The opposition teamed up with the Greens to block the bill, which would change the under-16s social media ban by doubling fines to $99 million for tech companies who breach the age restrictions.
It would also force the tech companies to hand over documents to the online safety watchdog.
The social media age restrictions passed with bipartisan support in December, but the proposal to tighten enforcement is yet to be backed by enough politicians to pass.
The prime minister said the lack of support was "extraordinary".
"We've always said there'd need to be adjustment to the legislation, that we wouldn't allow the perfect to be the enemy of the good, and we haven't done that," he told ABC Radio on Friday.
"The eSafety commissioner has said what she needs is more powers, powers to get documents, and powers to get the information from the big companies.
"This legislation is four pages, not complex, simple."
Platforms subject to the age restrictions include Instagram, TikTok, Snapchat and Reddit.
More than four in five Australians under-16s are still on social media, according to research by the British Medical Journal.
No penalties have yet been issued to tech companies for non-compliance.
A Senate inquiry into the bill will hand down a report in late August.
Opposition communications spokeswoman Sarah Henderson said while the bill does try to make the social media rules tougher, the coalition remained unconvinced they went far enough.
"This is a social media ban, which is failing ... a half-baked law, which is poorly designed, which was rushed, which is badly implemented, and which is not working," she told ABC Radio.
"We will interrogate this bill properly, and frankly, I think the amendments before the parliament need to be tougher."
