In recent years, the number of autistic people entering university has increased in Australia and worldwide. While an encouraging trend, autistic students' completion rates remain much lower than non-autistic students in Australia. Perhaps unsurprisingly, numerous studies investigating autistic people's experiences at universities have identified stigma and discrimination as a significant barrier facing autistic people in higher education. In this study, our team of autistic co-researchers and non-autistic researchers co-produced an in-depth qualitative study to understand the contexts and circumstances in which autistic people felt stigmatised or experienced discrimination at universities in Australia. We interviewed 21 autistic people who either had completed at least one university course, or were studying a university course, or had enrolled in but discontinued at least one university course in Australia. Using reflexive thematic analysis, we identified four themes: (1) 'My disability is something that people just don't have a clue about', (2) 'the system is really stacked against you', (3) the onus is on autistic students, and (4) 'grit and stubbornness'. Based on these findings, we suggested implementing Universal Design for Learning, neurodiversity-affirming and trauma-informed practices, together with a participatory approach to better design university curricula, processes, and support services for autistic students.