Damage in excess of deposit held

Tenancy Deposits

Hi a tenant recently passed away in my property and has left a significant amount of damage. After his demise I arranged for a an independent checkout so the damage is all recorded. I now find myself in a situation whereby the deposit ( which hasn’t been refunded ) falls significantly below the cost of repairs to return the flat to a habitable condition. I know the tenant was financially in a good position, so how/can I attempt to claim the refurbishment costs for my property ? Is a small claims court my best form of approach ? Your advice would be appreciated