A wide range of respiratory diseases, such as cold and flu, asthma, and COVID-19, affect people's daily lives worldwide. In medical practice, respiratory sounds are widely used in medical services to diagnose various respiratory illnesses and lung disorders. The traditional diagnosis of such sounds requires specialized knowledge, which can be costly and reliant on human expertise. Despite this, recent advancements, such as cough audio recordings, have emerged as a means to automate the detection of respiratory conditions. Therefore, this research aims to explore various acoustic features that enhance the performance of machine learning (ML) models in detecting COVID-19 from cough signals. It investigates the efficacy of three feature extraction techniques, including Mel Frequency Cepstral Coefficients (MFCC), Chroma, and Spectral Contrast features, when applied to two machine learning algorithms, Support Vector Machine (SVM) and Multilayer Perceptron (MLP), and therefore proposes an efficient CovCepNet detection system. The proposed system provides a practical solution and demonstrates state-of-the-art classification performance, with an AUC of 0.843 on the COUGHVID dataset and 0.953 on the Virufy dataset for COVID-19 detection from cough audio signals.