The SPIRE FTS Spectral Feature Finder (FF), developed within the Herschel Spectral and Photometric Imaging Receiver (SPIRE) Fourier Transform Spectrometer (FTS) instrument team, is an automated spectral feature fitting routine that attempts to find significant features in SPIRE FTS spectra. The $^3$P$_1$ - $^3$P$_0$ and $^3$P$_2$ - $^3$P$_1$ neutral carbon fine structure lines are common features in carbon rich far-infrared astrophysical sources. These features can be difficult to detect using an automated feature detection routine due to their typically low amplitude and line blending. In this paper we describe and validate the FF sub-routine designed to detect the neutral carbon emission observed in SPIRE spectral data.