In human-robot collaboration (HRC) for assembly, a robot needs to use its onboard vision systems to perform many sensing tasks. The robot's observations may not be always reliable due to erroneous sensing caused by limitations of the detection systems and disturbances. Hence, additional observations made by the robot or the human co-worker seem to be necessary. However, too much human involvement may increase human workload. Hence, allocation of autonomy through switching between autonomous and manual sensing (observation) modes seems to be reasonable. Bayesian sequential decision-making may be an approach to determine the optimal allocation of these modes in the presence of sensing uncertainties. However, optimal decision-making approaches such as the Bayesian approach may not necessarily fit with human's decision style. It has been shown that human regret plays a critical role in decision-making under uncertainty. It is rational for humans to make suboptimal choices to avoid regret. In this paper, we include human regret analysis in Bayesian decision-making in the automated allocation of sensing modes for detection of right assembly parts. We evaluate this approach in a human-robot collaborative assembly task. The experimental results show that regret-based human-like suboptimal allocation of autonomous and manual sensing modes improves human-robot interaction and assembly performance.