Margo (53) and George Sturrock (52) were on holiday when the blaze destroyed the outbuilding and most of the garden at their Larbert property.
However, the couple feel the incident on August 4 could have been prevented if Falkirk Council had rebuilt the fence which separates their George Street home from the public car park.
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George Sturrock said: “The fence was blown down a few years ago. It had prevented people from using our garden as a passageway to get to the next street.
“We don’t really understand why the council can’t pay for a new fence. If police do increase patrols this would be a positive step but it could just move the problem somewhere else.
“I feel they could be taking our concerns more seriously as the teenagers, who we believe caused the damage, need a place to hang out. This is an unsettling situation for us.”
It will cost the couple at least £2000 to replace their wooden shed with a concrete one.
Council neighbourhood officers say they are seeking legal advice to establish which party should be covering the cost of the damage.
Councillor David Grant is urging the local authority to find a solution.
He said: “The couple want the council to reinstate the fence and because it separated the house from the car park it is not clear who is responsible for paying for it.”