Georgina Barnett begged 46-year-old Thomas Brogan to stop as he struck her repeatedly on the head and body in the attack on June 25.
The widow, who had osteoporosis but led an independent life, was left with multiple bruises and a deep cut to the back of her head. She died five days later in hospital.
Unemployed Brogan pleaded guilty at the High Court in Edinburgh to murdering Mrs Barnett, a mother of one daughter, at her home in Ramsay Road, Kirkcaldy, Fife.
The court heard that the motive for the attack is unknown but in the hours before the assault Brogan appeared to have been angry with a drinking associate "in connection with a mobile phone".
On the evening of the attack, Brogan was heard shouting "Don't f****** lie to me, I'll f****** kill you" from within the victim's flat.
A neighbour also heard a terrified Mrs Barnett pleading with the accused, saying: "Tam, stop, please. Please stop."
The pensioner later asked police officers: "Why was he hitting me?"
Mrs Barnett's family are understood to be devastated by their loss and struggling to come to terms with the manner in which she died.
Mrs Barnett, known to her friends as Doddy, was a widow for around 30 years. She had lived in her flat for more than three decades and was well-known and liked in the local area.
She was physically frail but mentally alert and lived independently in her home.
The fatal attack happened at about 8.30pm on June 25.
The court heard that around 3pm that day, Brogan spoke to some of Mrs Barnett's neighbours. He was "extremely drunk and agitated, talking about a problem with his mobile phone and the sim card for it". From what they could tell, his anger appeared to be directed towards a man who was an associate of his, Bryan Hughes.
Later that evening, neighbours heard two dull thuds from Mrs Barnett's living room, then a loud crashing noise.
They heard the accused repeatedly shouting: "Don't f****** lie to me, I'll f****** kill you" and "stop taking the piss".
They rang police, believing Brogan was fighting with Mr Hughes in the flat, but were shocked to then hear Mrs Barnett's voice saying: "Tam, stop please."
When police arrived, they found Brogan at the flat with his hands covered in blood.
Mrs Barnett, on the floor in the corner of the living room, had severe facial injuries and was bleeding heavily from her head. Blood was spattered on a wall.
The victim was conscious and able to speak to police and paramedics at that stage.
On arrival at Victoria Hospital in Kirkcaldy, she told staff that Brogan had beaten her up and that he had been angry.
"He was angry with himself," she told staff.
The victim later told detectives he had come to her house drunk "looking for the boy next door". She expressed disbelief that he would do that to her "just because of that bloody sim card", the court heard.
Her condition worsened and she died on June 30. A post-mortem examination found injuries consistent with a sustained blunt force attack, including 11 fractured ribs and a fractured sternum.
Advocate depute Leanne Cross, prosecuting, said: "The scale and nature of the injuries, even allowing for her age, demonstrate a sustained and forcible attack."
She added: "Mrs Barnett's family are utterly devastated by their loss. They are finding it difficult to come to terms with the death of Mrs Barnett and the manner of it."
Brogan was detained at the scene by police. He told officers that day: "I done it. I done everything."
The court heard he had 10 previous convictions at summary level, mostly for dishonesty and public order offences.
His QC, Mark Stewart, told the court that Brogan apologises for what he did and is "mortified" by his conduct.
Speaking outside court, Mrs Barnett's nephew Thomas Johnstone, 62, said the death of the much-loved woman has had a big impact on the family.
He said: "She was a very sprightly 90-year-old. She would do everything in the house herself still. We're all still shocked."
Mr Johnstone, who was at his aunt's hospital bedside every night until she died, welcomed the guilty plea at the early stage.
He said: "It's a relief to us that we won't have to go through a trial. We hope that he gets a just sentence that he really deserves."
On Brogan's apology, he added: "An apology doesn't bring my auntie back. That's not good enough."
Brogan will be sentenced by judge Lord Pentland at the same court on October 30.