Task allocation research is often efficiency-focussed, but procedural and work-psychological perspectives are required to enable human-centred human–robot interaction (HRI). Hence, the motivational and cognitive outcomes of the degree of worker influence over task allocation are relevant to research objects for allocation process design. In a laboratory experiment, 87 participants manufactured goods in collaboration with a robot under three conditions: (1) a support system decided the allocation, (2) a support-system allocation could be revised, (3) the participant determined the allocation. Conditions affected mental effort, process control and autonomy, resulting in higher values when participants allocated tasks themselves. Satisfaction with the process appears lower with no worker influence. Trust in the support-system moderates the condition effect, with higher satisfaction depending on trust when a system is involved in allocation. An allocation made by the workers and adaptability is preferred. Results show the importance of worker influence over task allocation in HRI. Practitioner Summary: Our experiment on allocation processes seeks to satisfy the gap in human-centred psychological research on task allocation in human–robot interaction (HRI). For successful, ergonomic HRI, it is found that workers should be provided with influence over task allocation.