Golden Hillock School was put in special measures last month after criticisms over leadership.
It was one of 21 schools inspected by Ofsted over an alleged plot by some Muslims to take over schools.
The current governing body was only formed in December, governors said.
They said it meant there was not enough time to implement the government's anti-radicalisation strategy Prevent before a visit by Ofsted.
Inspectors criticised religious teaching at the school which they said focused almost exclusively on Islam.
Current governor Mohammed Shafique said: "We became a governing body on 4 December. We were in the process of trying to explore a lot of things and all of that came to a standstill on 31 March [Ofsted visit].
"We have done a lot to give young people a broader experience, I'm sure we could do a lot more. But we haven't been given enough chance to carry those actions through.
By Phil MackieNews Correspondent
On the day I visited Golden Hillock, two of the three classes I saw were being taught by supply teachers.
This was despite the school being barely 60% full due to Year 10 work experience and the end of GCSEs.
The governors estimate the school has a 20% vacancy rate which they say has been exacerbated by the Trojan Horse allegations.
They told me the number of resignations that were handed in before the end of May ran into double figures.
The school has struggled for a long time, although last year its academic results had shown significant improvement.
Last year it was advised by the DfE and Birmingham City Council to  become part of an academy and was directed towards the Park View Educational Trust, whose schools had been rated Outstanding.
Now the governors accept that they may be replaced and the school will be under new management, again, in the autumn.
"To be judged, you need to be given time to actually do something. We were not given enough time to do anything before a judgement was passed."
The four academies put in special measures last month - Golden Hillock, Nansen Primary, Park View and Oldknow - had until Friday to send in formal responses to the government detailing how they would make improvements, or face losing their funding and being taken over.
The city council has already submitted its action plan to the Department for Education (DfE) for the schools which it runs, which were also rated inadequate or given notices of improvement.
Mr Shafique said he would be happy to stand down as a governor if someone else could make improvements at Golden Hillock.
Fellow governor Mohammad Ashraf said it was difficult to see what the future held for the school.
"The honest answer is we don't know," he said.
"I do not know where we're going to be heading towards come September, or next year or even the next few days."
The BBC has also been told by a former governor, who asked not to be named, that the previous governing body of Golden Hillock opted not to take part in Prevent in 2010.
Inquiries by Birmingham City Council and the DfE into the so called "Trojan Horse" plot are due to publish their findings later in the summer.
Governors at one of the Birmingham schools at the centre of the "Trojan Horse" inquiry have said they were not given enough time to make improvements before a visit by Ofsted.