Liam Payne's sister has broken her silence after the tragic death of the One Direction star ... and her message is absolutely devastating.

Ruth Gibbins posted a lengthy statement to her Instagram page along with several sweet photos of the siblings -- all to express how much she loved her brother and her unbearable pain, which included, "I'm sorry I couldn't save you."

She began with, "I don't believe this is happening. Many times have I poured my heart out publicly with pride about Liam but never much about life as his sister ... Liam is my best friend."

After expressing how much Liam loved his family, friends and being a member of One Direction, she shared her heartbreaking reflection -- saying, "I don't feel this world was good enough or kind enough to you."

She continued ... "You just wanted to be loved and to make people happy with your music. You never believed you were good enough, I hope you can now see this outpouring of love that you never received in your time."

Ending her post with the tearjerker ... "I'm sorry I couldn't save you" ... Ruth promised she would help take care of his young son, Bear, and make sure the child knew "how much you idolize him."

Liam's father recently shared his grief with his son's fans in Argentina ... standing with them in an incredibly poignant moment right outside the hotel on Friday evening where Liam died.

As TMZ previously reported ... authorities in Buenos Aires are awaiting test results on the narcotics and meds they recovered from Liam's hotel room where police say he jumped to his death on Wednesday.