John Michael Holdsworth, a maintenance engineer with Brighouse Borough Council and later Calderdale Council, worked with asbestos-covered pipes in swimming pools at Sowerby Bridge and Brighouse in the 1980s.
At an inquest yesterday, West Yorkshire coroner Roger Whitaker said 71-year-old Mr Holdsworth, of Arnold Royd, had died of industrial disease - bronchial pneumonia caused by mesothelioma.
Mr Holdsworth's wife Ariel, 62, said: "It makes me so angry. I could have had another 20 years with Michael. He had no other medical problems. I want someone to take responsibility for his death, because it certainly wasn't his fault."
Mrs Holdsworth is hoping other families who may have lost a loved one through working with asbestos will come foward and get help.
She said: "There must be loads of people out there who have lost people through asbestos and there is help out there. It won't bring Michael back. Nothing will do that. We've lost him but we can still fight for what's right."
Daughter Jane Donlan, 43, from Cleckheaton, said: "I feel angry my father was put in a situation by the council that ultimately caused his death. The coroner has ruled that my father died from industrial disease and someone should accept responsibility for that. We've got to put it in the hands of solicitors now and see what happens."
The family's case is being handled by John Pickering and Partners, a Halifax firm specialising in asbestos disease compensation claims.
Mr Holdsworth's former work colleague, Stanley Shaw, said they had removed asbestos insulation from pipes in swimming pools and had generally worked with the deadly substance over a number of years.
A council spokesman said: "The council would like to express its sympathy to the family and friends of Mr Holdsworth. The case is now in the hands of legal representatives."