Sarcasm is a language phenomenon usually employed to express negative sentiments in a humorous or critical manner. Although sarcasm is a widely used communication tool, it is often challenging to comprehend. The existing approaches for detecting sarcastic sentiments are mainly designed for English language text, and the study of low-resource languages has gained significant attention among scholars. Hence, this research aims to identify sarcasm in Twitter posts that include sentences in Tamil and Telugu languages. This paper presents the first effort to create two distinct datasets for sarcasm detection in Telugu and Tamil languages by scraping tweets from Twitter, thereby addressing the lack of such resources in these languages. To analyze sarcasm in Tamil and Telugu tweets, we proposed a variety of methodologies. These included machine learning models like Decision Tree, Naive Bayes, Logistic Regression, Support Vector Machine, and Random Forest as well as sophisticated neural network techniques like Convolutional Neural Networks and Long Short-Term Memory. Our findings show that the Telugu and Tamil datasets achieved an accuracy rate of 95.68% and 95.37%. The results provide a better understanding of the use of sarcasm in low-resource languages and offer a foundation for further research in this field. This research paper contributes to the field of natural language processing by demonstrating the effectiveness of the proposed methodologies in identifying sarcasm in Tamil and Telugu tweets.