A drying installation had been set alight.
Dalton said such incidents were "soul destroying" for staff who worked hard to ensure the city's amenities were kept clean and maintained.
"They work hard to keep Napier up to scratch then someone comes along and does this."
The cost to repair, replace and carry out paintwork would effectively fall on ratepayers, Dalton said.
"So this hits everyone."
As well as the cost of repairs there was the inconvenience of having to close the facility to the public.
"We are set to start work on the Destination Playground at Anderson Park so you start to get nervous about vandalism - what will they do to it?"
Dalton did not think the situation had got any worse though.
"It has always been there so people have to be vigilant - we need to work to stamp this sort of thing out."
He said anyone seeing any suspicious activity, or who may have come across information about who may have been responsible for carrying out vandalism, needed to make contact with council or the police.
Police took the same "call us straight away" stance.
In the case of the Anderson Park incident a check of the building showed someone had later scrawled in black marker pen on the wall by the door "Jack did this".
Anyone with any information about the fire can call the confidential Crimestoppers on 0800 555 111.