Semiconductor quantum dot (QD) structures are considered as promising building block for spintronic applications with the advantage of prolonged spin relaxation time owing to 0D character of confined carriers or excitons. However, feasible application is haunted by severe spin injection loss from its adjacent barrier layers and its mechanism is still not fully understood. Here, we show that exciton spin injection in self-assembled InAs/GaAs QD molecular structures (QMSs) is dominated by localized excitons confined within the QD-like regions of the wetting layer (WL) and GaAs barrier layer surrounding QD structures. The origin of spin injection loss is attribute to finite anisotropic exchange interaction (AEI) of the localized excitons subjected to asymmetric confinement potential in the injection layers. As a result, the AEI of the injected excitons and, thus, the spin injection efficiency is determined to be correlated with the overall geometric symmetry of QMSs, which hold strong influence on the confinement potential of the localized excitons in the surrounding barrier layers. Our results shed light on the microscopic origin of the spin injection loss in QD structures. More importantly, they offer a useful guideline to significantly improve spin injection efficiency by optimizing the lateral arrangement of QMSs and overcome a major challenge in the QD based spintronic device applications.