Shannon Gallagher, from County Donegal was found on Thursday by foster carers she had been placed with, hours after telling them that she was going to bed.
Her sister Erin died on October 27 after taking her own life, reportedly while she babysat her four-year-old brother. At the time of Erin's death, allegations circulated that she had been the victim of cyber bullying.
Father John Joe Duffy, who spoke at the funeral, said the Government must take urgent action to prevent further tragedies.
"Society has failed two children, two sisters within two months and that is a most damning indictment for any society evidenced by the second white coffin that is before this altar within two short months, 45 days ago to be exact," said Fr Duffy.
"My heart is devastated. My heart is shattered at how poorly we understand the issues concerning youth mental health and mental health issues in the general population in Ireland. And the terrible consequences we see occurring and re occurring on a regular basis though out the country."
Gardai have been investigating claims of cyber bullying and it is understood a number of teenagers have been interviewed by officers.
The girl's grandfather, James Gallagher, described Erin as an amazing girl and her death as 'a waste of a life' in the weeks after the tragedy. He said Shannon had been missing her younger sister.
After Shannon's death, hundreds of people packed into St Mary's Church in Stranorlar to pay their last respects to the schoolgirl. It was the same church many of the mourners had filled for Erin's funeral in October.
Fr Duffy said: "None of us wanted and none of us expected to find ourselves back in this church today to be once again praying this Mass for a 15-year-old child Shannon so soon after the death of 13-year-old sister Erin.
"We are numb and in such a state of shock and unrealness, total disbelief that for the second time within two months that (the girls' mum) Lorraine and the Gallagher family are having to face the desperate pain and deep anguish of losing such a beautiful child in the most tragic of circumstances.
"The systems and methodologies in place and used by the HSE (Health Service Executive) and other agencies and professionals dealing with these cases simply does not work. We are failing to protect the most fragile and most vulnerable children in our society.
"We are failing to bring in the children, young people and most vulnerable adults on the margins of our society to the safety of the centre where they ought to find support, comfort, and safety.
"Hiding behind professionalism and qualifications or the inertia of being able to change rules, legislation or regulations is simply not acceptable, when so many lives getting younger have being tragically and needlessly lost.
"I am now calling upon someone in Government to take a hands on role and to do what it takes. The time for talking is over.
"For the sake of all people on the margins or in similar circumstances, for the love of God let some one person in Government take leadership and reform what is clearly a broken system."