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Deep neural networks struggle to continually learn multiple sequential tasks due to catastrophic forgetting of previously learned tasks. Rehearsal-based methods which explicitly store previous task samples in the buffer and interleave them with the current task samples have proven to be the most effective in mitigating forgetting. However, Experience Replay (ER) does not perform well under low-buffer regimes and longer task sequences as its performance is commensurate with the buffer size. Consistency in predictions of soft-targets can assist ER in preserving information pertaining to previous tasks better as soft-targets capture the rich similarity structure of the data. Therefore, we examine the role of consistency regularization in ER framework under various continual learning scenarios. We also propose to cast consistency regularization as a self-supervised pretext task thereby enabling the use of a wide variety of self-supervised learning methods as regularizers. While simultaneously enhancing model calibration and robustness to natural corruptions, regularizing consistency in predictions results in lesser forgetting across all continual learning scenarios. Among the different families of regularizers, we find that stricter consistency constraints preserve previous task information in ER better.