Cupar Children’s Gala organising committee said “every safety precaution was risk assessed” for the event.
A full investigation into the incident will be carried out by organisers, and the Health and Safety Executive will undertake its own probe.
Critics have said the inflatable should never have been erected in such bad conditions.
Castlehill Primary School Association chairman Joe King called for calm.
He said on Facebook: “People are such experts after the event. The gala and most other public events are organised by a volunteer committee of normal people with normal jobs and families.
“No matter how many risk assessments you complete or HSE experts you employ, accidents will happen.
“An external vendor was employed by the committee.”
Liberal Democrat Cupar Fife councillor Margaret Kennedy said: “Many people will be hurting, emotionally and physically, after the events at the end of what was another super children’s gala.
“I have already spoken with the chair and offered my support where she feels it would be useful.”
North East Fife SNP MP Stephen Gethins also attended the gala. He said his thoughts were with all of those affected.
Former Fife journalist Eleanor Porter, 37, of Dunshalt, had her back to the inflatable slide when the drama unfolded.
She was watching her six-year-old son Magnus on a neighbouring fun house and her four-year-old daughter Phoebe had just come down the slide.
“I turned around and the slide had gone,” she said.
“Kids were thrown around flat out on the grass. There was quite a commotion. Phoebe was thrown quite a distance. She had been up a couple of times.
“Another wee girl had just come off. She was hit from behind by the slide and knocked into a neighbouring funfair ride where she smashed her head.”