Leonard Debell, 78, and his wife were on their way to meet friends for lunch in June 2010 when he fell over a small lump of concrete protruding from the base of a traffic bollard which had been hit by a car.
Mr Debell, who suffered a hernia and an injured shoulder, sued the Dean and Chapter of England's second oldest cathedral and was awarded the compensation at Lewes County Court in April last year.
The damages were reduced by 20% to reflect Mr Debell's contributory negligence in not taking sufficient care to see where he was walking.
On Wednesday, two judges in London allowed the cathedral's appeal against the ruling that it was to blame.
Lord Justice Elias, sitting in the Court of Appeal with Lady Justice Hallett, said: "This was a most unfortunate accident but not one for which the cathedral should be liable."
He said they accepted the argument that the County Court did not apply the foreseeability test in the appropriate way.
The question for the judge was whether the piece of concrete created a danger of a kind which the cathedral authorities were required to address.
Lord Justice Elias added: "This was an extremely small piece of concrete which could not be said to pose a real danger to pedestrians. It would be very unlikely that a pedestrian would walk so close to the bollard, even approaching it at an angle, or that he would injure himself if he did.
"Accordingly, even if, contrary to my view, the judge did apply the right test, then in my judgment his conclusion was not open to him."
