Homeowner Richard Brown said he was outraged by the decision and has asked that police review the way officers have handled their dealings with him and Keenan.
He said he had built the concrete post in accordance with a formal survey of the property and had placed it on the survey pegs. The post was then built to form the corner of the property.
He said he arrived at the property - which is being renovated - to find the concrete post smashed and a roading crew saying his neighbour had destroyed it with a sledgehammer.
Brown said he called 111 to report the damage and directed officers to Keenan. He said officers then visited him to say no charges would be laid and the issue between the men was "a civil matter".
The root of the row lies in the breakdown of a relationship between Brown and his former partner - the sister of the woman Keenan lives with.
The relationship ended about three years ago and Brown sold the house he jointly owned with her. The house, between his home and Keenan's, has led the men to a number of disputes.
On one occasion, the men became involved in a pushing match over a set of windows. Brown claimed he had been assaulted by Keenan. After 111 was dialled, officers who attended told Brown that Keenan claimed he had been assaulted.
Brown said the police had been called five times in 18 months. He said he was phoned by a senior sergeant who ran the local policing area last week to say there were internal efforts underway to stop the men from clashing.
Criminal lawyer Gary Gotlieb said the destruction of another person's belongings on their property was a criminal charge called wilful damage.
He said the description "civil dispute" was an attempt to push the issue towards civil courts. It meant people would have to take their own court action. "That's a cop out."