Deep sleep staging networks have reached top performance on large-scale datasets. However, these models perform poorer when training and testing on small sleep cohorts due to data inefficiency. Transferring well-trained models from large-scale datasets (source domain) to small sleep cohorts (target domain) is a promising solution but still remains challenging due to the domain-shift issue. In this work, an unsupervised domain adaptation approach, domain statistics alignment (DSA), is developed to bridge the gap between the data distribution of source and target domains. DSA adapts the source models on the target domain by modulating the domain-specific statistics of deep features stored in the Batch Normalization (BN) layers. Furthermore, we have extended DSA by introducing cross-domain statistics in each BN layer to perform DSA adaptively (AdaDSA). The proposed methods merely need the well-trained source model without access to the source data, which may be proprietary and inaccessible. DSA and AdaDSA are universally applicable to various deep sleep staging networks that have BN layers. We have validated the proposed methods by extensive experiments on two state-of-the-art deep sleep staging networks, DeepSleepNet+ and U-time. The performance was evaluated by conducting various transfer tasks on six sleep databases, including two large-scale databases, MASS and SHHS, as the source domain, four small sleep databases as the target domain. Thereinto, clinical sleep records acquired in Huashan Hospital, Shanghai, were used. The results show that both DSA and AdaDSA could significantly improve the performance of source models on target domains, providing novel insights into the domain generalization problem in sleep staging tasks.