Hannah Smith, 14, from Lutterworth, Leicestershire, killed herself on Friday after being bullied on website ask.fm, her father Dave said.
Her older sister Jo, 16, told the Daily Mirror how she is now being subjected to the same hateful taunts her sister was as they prepare for her funeral.
“I’ve just lost my sister and now I’ve got to deal with getting abuse myself,” she told the Mirror.
“These trolls don’t care what happened to Hannah or what we’re going through, they just live in their sad little worlds.
“It’s really upsetting. I’m struggling to cope with what’s happened and don’t need these trolls hounding me.”
Jo described her sister as “a beautiful person and so full of life and love”.
Mr Smith said the schoolgirl was found dead in her bedroom by Jo.
Website ask.fm has described Hannah’s death as a “true tragedy” and promised to work with police investigating the incident.
The question-and-answer site allows users to send messages to one another without their identity being disclosed.
Although users have to register an email address, name and date of birth, those posting messages can choose to do so anonymously.
A spokeswoman for ask.fm said in a statement: “Hannah Smith’s death is a true tragedy; we would like to convey our deepest condolences to her family and friends.
“We have reached out to the Leicestershire police and would be happy to co-operate with their investigation into the true circumstances of her suicide.
“Ask.fm actively encourages our users and their parents to report any incidences of bullying, either by using the in-site reporting button, or via our contact page.
“All reports are read by our team of moderators to ensure that genuine concerns are heard and acted upon immediately - and we always remove content reported to us that violates our Terms of Service.”
Mr Smith, 45, a lorry driver, called on David Cameron to put regulations in place on social networking websites such as ask.fm, to try to prevent another tragedy.
He is urging the authorities to close down the site, and those like it, after stumbling across cruel taunts from so-called “trolls” which he said drove his daughter to take her own life.
He told the Leicester Mercury: “Websites like this are bullying websites because people can be anonymous.
“If I had not spoken up about this, another teenager could be dead next week.
“Ask.fm and sites like these are making millions out of people’s misery and it is wrong.
“I would appeal to David Cameron as a Prime Minister and a father to look at this to make sure these sites are properly regulated so bullying of vulnerable people like my daughter cannot take place.
“I don’t want other parents to go through what I am going through.”
Hannah’s father described his devastation over his daughter’s death, who many described as popular and bright.
He said: “We sleep downstairs now, we don’t have a bedtime.
“Since this happened I have only had three hours’ sleep a night.
“I want this to be sorted out as soon as possible so no other vulnerable children die.
“Hannah was a bubbly, happy person.
“She was colourful, she was a normal teenager and was very, very happy.
“For Hannah to do something like this... We never expected this. We never saw any signs of her doing this.
“I have now got to concentrate on burying my daughter. I need to be left alone to bury her and to grieve properly for her.”
Nora Parker, headteacher at Lutterworth High School, said the staff and students were deeply upset at hearing news of her death.
She said: “The governors, staff and students of Lutterworth High School were deeply shocked and saddened to learn the news that on 2nd August Hannah Smith, a Year 9 student, took her own life.
“Hannah, who just completed her final year at the school and was looking to transfer to Lutterworth College in August, was a bright, bubbly, popular and thoughtful girl who was liked and respected by all those she came into contact with.
“She had everything to live for and her family, who are utterly devastated, are at a loss to understand why this has happened.”
More than 45,000 people have offered their support and “liked” a Facebook page set up in tribute to Hannah.
It says on the page: “Hannah Smith; a beautiful young girl who everyone loved very much; who decided to take her own life after being bullied; we will miss you princess; loveyou”
A petition - available from https://submissions.epetitions.direct.gov.uk/petitions/48886 - calls for greater measures to tackle websites like ask.fm.
It states: “Cyberbullying has been an ever increasing problem within the UK for a considerable amount of time, with one of the biggest offenders becoming ask.fm, a site popular amongst young people where posts can be made with confidence anonymously which has led to bullying, mental health problems and suicides as well as grooming.”
Organisations that tackle bullying called on internet service providers to work with Government, police and schools to address online abuse.
Emma-Jane Cross, from campaign group BeatBullying, said: “We cannot stand by while innocent children lose their lives. Adults need to set an example for young people and we all have a responsibility to tackle this type of behaviour and keep our children safe.
“We want internet service providers, schools, Government and the police to come together and produce a UK anti-bullying strategy, to prove that this kind of behaviour will not be tolerated.”
Peter Wanless, chief executive of the NSPCC, said: “This is a tragic case where Hannah felt like she had no other option but to end her life. The cruel nature of cyberbullying allows perpetrators to remain anonymous and hide behind their screens.
“This is something that must be tackled before it gets out of hand. We must ensure young people have the confidence to speak out against this abuse, so that they don’t feel isolated and without anywhere to turn.”
Hannah’s death comes amid a growing row about the policing of social media after rape and even bomb threats were made to high-profile female media personalities on Twitter.
Television classicist Mary Beard said that she has received numerous “threats of violence and death” on the social media site in recent days.
Andy Trotter, head of the Association of Chief Police Officers’ communications advisory group, told BBC Breakfast yesterday: “I think there is a responsibility from everyone here.
“Twitter clearly have one - they are the ones who set the platform up, they are the ones who have got to make sure that people are safe on that platform and there’s a means by which people who break their code or break the law are taking off that system swiftly and are not allowed back on there.
“If it then falls into the more serious matters, these ones we have heard of of late, ones that turn into credible threats against individuals or a course of harassment against people, that’s a matter for the police to investigate.”