It follows complaints from ex-Formula One boss Max Mosley about the difficulty he faced in getting a video removed from the internet.
The search giant argued it was not its job to monitor net content.
The cross-party committee said this argument was "totally unconvincing".
The report by a committee of MPs and peers was commissioned by the government to look into privacy and free speech issues after a series of high profile super-injunctions were made public last year.
Celebrities including Ryan Giggs found that gagging orders against newspapers were routinely flouted online. In Mr Giggs' case, the details of his super-injunction were mentioned at least 75,000 times on Twitter, the committee said.
Its report said that online firms needed to be brought in line with offline media in such cases.
"We recommend that, when granting an injunction, courts should be proactive in directing the claimant to serve notice on internet content platforms such as Twitter and Facebook," it said.
Some of the harshest criticism was reserved for Google.
"Where an individual has obtained a clear court order that certain material infringes their privacy and so should not be published, we do not find it acceptable that he or she should have to return to court repeatedly in order to remove the same material from internet searches," the report said."
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