An online petition started by parents, in response to the risk of the nursery closing earlier this year, received more than 1,400 signatures.
A statement alongside the petition said the report from Ofsted was not accurate and did not “reflect the true quality of care provided”.
It said: “The inspection was not carried out appropriately for a forest school setting, with criteria applied that are more suited to standard indoor nurseries.”
This led to an “unfair and unbalanced assessment”, the petition added.
According to Sheffield City Council, Forest School Kindergartens had made its decision to close the nursery on 29 August before the publication of the second Ofsted report.
Councillor Dawn Dale, head of education, said the authority – which was not connected to Ofsted – had been working closely with the nursery to manage the closure.
Dale said: “Our priority has been to ensure children attending the setting continue to be well cared for, have access to learning and remain safe while at nursery.”
The council emphasised it had not cut the nursery’s early years funding after the inadequate rating, despite that being a statutory requirement after such a rating.