Molly's father, Ian Russell, said: "I have no doubt that social media helped kill my daughter."
Speaking to ITV on Friday, he said: "painfully we saw what Molly had been exposed to online only after her death... deep into her depression, (it) heightened her anxiety, and led her towards a path of self-harm and suicide."
In the report, the Royal College of Psychiatrists said a proposed 2% levy on the UK revenues of major tech companies does not go far enough.
Instead, it wants the so-called “turnover tax” to apply to international turnover and for some of the money from it to be used for mental health research.
Molly’s father, Ian Russell, spoke of the urgent need for greater action in an emotional foreword to the report, in which he described the “wrecking ball of suicide” that “smashed brutally” into his family, blaming “pushy algorithms”.
Speaking to ITV on Friday, he said his family regularly had meetings about online safety before Molly's death.
"The addiction and that 'safe world' that a teenager like Molly might feel that she finds online with like-minded people just deepens that isolation and makes it even harder for her to reach out," he said.
He said he found on her social media accounts bleak "black-and-white memes", graphic self-harm content and "suicide-encouraging" material that he felt encouraged depressive thoughts.
Mr Russell also detailed one of Molly’s final notes which described how she felt “with heart-breaking clarity”.
“I’m the weird sister, quiet daughter, depressed friend, lonely classmate,” she wrote.
“I’m nothing, I’m worthless, I’m numb, I’m lost, I’m weak, I’m gone. I’m sorry. I’ll see you in a little while. I love you all so much. Have a happy life. Stay strong xxx.”
Dr Bernadka Dubicka from the Royal College of Psychiatrists on the dangers of social media for people with mental ill health
While welcoming the UK Government’s White Paper on online harms, the College’s report calls for an independent regulator with powers to be able to establish a protocol for the sharing of data from social media companies with universities for research, such as behavioural data.
It also points to evidence that increased social media use may result in poorer mental health, particularly in girls.
Dr Bernadka Dubicka, chairwoman of the child and adolescent faculty at the Royal College of Psychiatrists and co-author of the report, said: “As a psychiatrist working on the front line, I am seeing more and more children self-harming and attempting suicide as a result of their social media use and online discussions.
Speaking to ITV, she said: "They're not directed towards positive support or alternative sources of information, they just give them more and more of the same."
Dr Bernadka Dubicka said in the report: “We will never understand the risks and benefits of social media use unless the likes of Twitter, Facebook and Instagram share their data with researchers.
“Their research will help shine a light on how young people are interacting with social media, not just how much time they spend online.
“Self-regulation is not working. It is time for Government to step up and take decisive action to hold social media companies to account for escalating harmful content to vulnerable children and young people.”
Claire Murdoch, NHS national director for mental health, said: “If these tech giants really want to be a force for good, put a premium on their users well-being and take their responsibilities seriously then they should do all that they can to help researchers better understand how they operate and the risks posed – until then they cannot confidently say whether the good outweighs the bad.”
The biggest social network, Facebook, said it is “already taking a number of the steps recommended” in the report.
“We remove harmful content from our platforms and provide support for those who search for it,” a spokesman said.
“We are working closely with organisations such as the Samaritans and the Government to develop industry guidelines in this area.”
A Government spokesman said: “We are developing world-leading plans to make the UK a safer place to be online. This includes a duty of care on online companies, overseen by an independent regulator with tough enforcement powers, to hold them to account.
“The regulator will have the power to require transparency reports from companies outlining what they are doing to protect people online. These reports will be published so parents and children can make informed decisions about their internet use.”