With the increasing prevalence of Web-based platforms handling vast amounts of user data, machine unlearning has emerged as a crucial mechanism to uphold users' right to be forgotten, enabling individuals to request the removal of their specified data from trained models. However, the auditing of machine unlearning processes remains significantly underexplored. Although some existing methods offer unlearning auditing by leveraging backdoors, these backdoor-based approaches are inefficient and impractical, as they necessitate involvement in the initial model training process to embed the backdoors. In this paper, we propose a TAilored Posterior diffErence (TAPE) method to provide unlearning auditing independently of original model training. We observe that the process of machine unlearning inherently introduces changes in the model, which contains information related to the erased data. TAPE leverages unlearning model differences to assess how much information has been removed through the unlearning operation. Firstly, TAPE mimics the unlearned posterior differences by quickly building unlearned shadow models based on first-order influence estimation. Secondly, we train a Reconstructor model to extract and evaluate the private information of the unlearned posterior differences to audit unlearning. Existing privacy reconstructing methods based on posterior differences are only feasible for model updates of a single sample. To enable the reconstruction effective for multi-sample unlearning requests, we propose two strategies, unlearned data perturbation and unlearned influence-based division, to augment the posterior difference. Extensive experimental results indicate the significant superiority of TAPE over the state-of-the-art unlearning verification methods, at least 4.5$\times$ efficiency speedup and supporting the auditing for broader unlearning scenarios.