Heart murmurs are abnormal sounds caused by turbulent blood flow in the heart. Several diagnostic methods are available to detect heart murmurs and their severity, including cardiac auscultation, echocardiography, and phonocardiography (PCG). However, these methods have limitations, including the need for extensive training among healthcare providers, the cost and accessibility of echocardiography, and noise interference during PCG data processing. This study proposes an end-to-end real-time heart murmur detection approach using traditional and depthwise separable convolutional networks. We applied a Butterworth filter and Continuous Wavelet Transform (CWT) to eliminate noise and extract meaningful features from the PCG data. The proposed network consists of three parts: a Squeeze net that generates a compressed data representation, a Bottleneck layer that minimizes computational complexity using depthwise-separable convolutions, and an Expansion net that up-samples the data to capture fine details. We evaluated our model on the publicly available CirCor pediatric heart sound dataset. Using only $\sim$5.4k parameters, we achieved an accuracy of 85%, a sensitivity of 85%, and a specificity of 92%, successfully outperforming several larger models. Furthermore, we converted our network into a TinyML format and tested it on two resource-constrained devices, achieving an average real-time inference accuracy of 91% on a Raspberry Pi 4B and 80% on an Android smartphone. The proposed lightweight model offers a robust deep learning framework for accurate, real-time heart murmur detection, showing strong promise for accessible medical diagnostics in limited-resource environments. The code is publicly available at https://github.com/jobayer/FunnelNet.