Resident Leith Power told councillors that some who had lived in the streets for four decades "never knew it was called Richmond Park".
Mr Power said children and families used it for recreation and the elderly used it as a walkway up what is a steep street.
"There appears to be no need for extra housing in the area. There are still undeveloped sections for sale as well as many houses and rental properties," he said.
Mayor Annette Main told the petitioners that it was council policy to divest some surplus property to reduce debt and this was about the beginning of a such a process.
"But this reaction shows that this reserve is well loved," Ms Main said.
The committee assured locals that they will be kept fully informed and consulted in future.