We analyze socio-psychological process wins and losses in relation to Human-AI collaborative performance. The reported heterogeneous effects of the body of literature on group performance in relation to structural and processual determinants are briefly summarized. Based on this, two of the most relevant socio-psychological aspects of Human-AI collaborative performance are highlighted: Accuracy of the shared mental model and fulfillment of basic human needs. The paper concludes by proposing an empirical and experimental research program that addresses under-researched socio-psychological phenomena in Human-AI collaboration that can be held accountable for process wins and losses.