We present STFTCodec, a novel spectral-based neural audio codec that efficiently compresses audio using Short-Time Fourier Transform (STFT). Unlike waveform-based approaches that require large model capacity and substantial memory consumption, this method leverages STFT for compact spectral representation and introduces unwrapped phase derivatives as auxiliary features. Our architecture employs parallel magnitude and phase processing branches enhanced by advanced feature extraction mechanisms. By relaxing strict phase reconstruction constraints while maintaining phase-aware processing, we achieve superior perceptual quality. Experimental results demonstrate that STFTCodec outperforms both waveform-based and spectral-based approaches across multiple bitrates, while offering unique flexibility in compression ratio adjustment through STFT parameter modification without architectural changes.