The NAHT, which was supported by two other teachers' unions, had its legal action thrown out by the High Court on Monday.
But the union said the failure of its legal challenge did not detract from its concerns about the potential impact of Ofsted's new system on the mental health and wellbeing of school leaders and staff.
General secretary Paul Whiteman said the union "will now consider an appeal" and will consult its members on industrial action.
Sir Martyn said he was pleased with the outcome of Monday's hearing, and that Ofsted had "consulted extensively" on its proposals, which will now roll out this month as planned.
Ofsted's new inspection framework is based on a "traffic light system" which will grade schools on several areas of school life, as well as on safeguarding.
The launch was pushed back to accommodate a consultation on the proposals, which included 6,500 responses.
The NAHT told the hearing that it wanted a narrative-only approach to inspections, similar to the way it works in Wales. Estyn, the Welsh school inspectorate, has removed judgements such as excellent and good, with reports instead providing a detailed summary of key findings which highlight a school's strengths and areas for improvement.
The NAHT also claimed that wellbeing was not taken into account in Ofsted's development of its plans.
But Ofsted's barrister Sir James Eadie told the court wellbeing issues were "absolutely in Ofsted's eyeline".
The new framework, with its altered grading system, also had the "overwhelming backing" of parents, he said.