The provider warns that the cuts will affect successful courses, and that the Teacher Training Agency's "draconian" procedures could drive other universities out of teacher education.
The TTA plans to halve Exeter's primary places after a primary English undergraduate course failed an OFSTED inspection. The agency, which is obliged by law to link funding to course quality, is currently consulting on how to relate inspection findings to next year's allocations.
The criticised course was already scheduled for closure and took its last students in October. However, the TTA cuts will apply to all Exeter's primary courses, despite good inspection reports.
A spokesman for the university criticised the process "that can produce sch draconian and disproportionate consequences".
Vice-chancellor Sir Geoffrey Holland said: "We informed the TTA at every opportunity that the scale of the cuts could not be confined to the course where problems had been identified, but would impact on other areas of provision, including those which OFSTED and the TTA have identified as being of excellent quality."
He said the system created instability which made it impossible to effectively plan to deliver high-quality initial teacher training.
A spokesman for the TTA said: "The agency welcomes the court's finding that its decisions in respect of both the initiation of procedures to withdraw Exeter's accreditation as an initial teacher training provider and the reduction of its primary ITT intake targets were reasonable and consistent with the agency's statutory obligations."