Self-deprecating sarcasm is a special category of sarcasm, which is nowadays popular and useful for many real-life applications, such as brand endorsement, product campaign, digital marketing, and advertisement. The self-deprecating style of campaign and marketing strategy is mainly adopted to excel brand endorsement and product sales value. In this paper, we propose an LSTM-based deep learning approach for detecting self-deprecating sarcasm in textual data. To the best of our knowledge, there is no prior work related to self-deprecating sarcasm detection using deep learning techniques. Starting with a filtering step to identify self-referential tweets, the proposed approach adopts a deep learning model using LSTM for detecting self-deprecating sarcasm. The proposed approach is evaluated over three Twitter datasets and performs significantly better in terms of precision, recall, and f-score.