Peter Bunyan, 53, of Brooklands Road, Cosby, pleaded guilty to manslaughter on the grounds of diminished responsibility at Derby Crown Court.
The court heard a witness saw him forcing entry into 84-year-old Brian Robson's house on 23 February.
Police then found Mr Robson with fatal head injuries. Bunyan will be sentenced at a later date.
Police told the court they arrived at the address to find Mr Robson in the hall and attempts to revive him failed.
Bunyan had returned to his house next door and was arrested there.
Det Insp Chris Barratt, from Leicestershire Police, said: "Bunyan's actions on that tragic day led to the death of a very much loved family man and devastated a family.
"I would like to offer my condolences to the family and thank them for their co-operation and understanding throughout our investigation and subsequent court proceedings."

Proposals for the upgraded tennis court at Anmer House would see it moved from its current position to improve views from the hall.
The new court, on the Queen's Sandringham Estate in Norfolk, would would be resurfaced with astroturf, says the application.
King's Lynn Borough Council will consider the plans at a later date.
The application, lodged by the Estate Office at Sandringham, says the "current tennis court needs extensive work to resurface" and it would make sense to "remove all the existing court and start again".
It says: "On completion of the new court, the garden will be prepared to reinstate the fencing and re-erect parkland iron fencing."
The Royal couple are known to be fans of tennis and have previously been spotted attending games at Wimbledon.
A Leicestershire man has admitted killing his neighbour after kicking down his front door.
[NEXT_CONCEPT]
Plans to revamp the tennis court at the Duke and Duchess of Cambridge's country mansion have been submitted.