Deep sequence recognition (DSR) models receive increasing attention due to their superior application to various applications. Most DSR models use merely the target sequences as supervision without considering other related sequences, leading to over-confidence in their predictions. The DSR models trained with label smoothing regularize labels by equally and independently smoothing each token, reallocating a small value to other tokens for mitigating overconfidence. However, they do not consider tokens/sequences correlations that may provide more effective information to regularize training and thus lead to sub-optimal performance. In this work, we find tokens/sequences with high perception and semantic correlations with the target ones contain more correlated and effective information and thus facilitate more effective regularization. To this end, we propose a Perception and Semantic aware Sequence Regularization framework, which explore perceptively and semantically correlated tokens/sequences as regularization. Specifically, we introduce a semantic context-free recognition and a language model to acquire similar sequences with high perceptive similarities and semantic correlation, respectively. Moreover, over-confidence degree varies across samples according to their difficulties. Thus, we further design an adaptive calibration intensity module to compute a difficulty score for each samples to obtain finer-grained regularization. Extensive experiments on canonical sequence recognition tasks, including scene text and speech recognition, demonstrate that our method sets novel state-of-the-art results. Code is available at https://github.com/husterpzh/PSSR.