We present deep spectrophotometry of several H II regions in the nearby low-mass spiral galaxies NGC 300 and M33. The data have been taken with Ultraviolet-Visual Echelle Spectrograph and Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy spectrographs attached to the 8-m Very Large Telescope and 10.4-m Gran Telescopio Canarias telescopes, respectively. We have derived precise values of the physical conditions for each object making use of several emission line-intensity ratios. In particular, we have obtained direct determinations of the electron temperature in all the observed objects. We detect pure recombination lines (RLs) of C II and O II in several of the H II regions, permitting to derive their C/H and C/O ratios. We have derived the radial abundance gradient of O for each galaxy making use of collisionally excited lines (CELs) and RLs, as well as the C and N gradients using RLs and CELs, respectively. We obtain the first determination of the C/H gradient of NGC 300 and improve its determination in the case of M33. In both galaxies, the C/H gradients are steeper than those of O/H, leading to negative C/O gradients. Comparing with similar results for other spiral galaxies, we find a strong correlation between the slope of the C/H gradient and MV. We find that some H II regions located close to the isophotal radius (R25) of NGC 300 and M33 show C/O ratios more similar to those typical of dwarf galaxies than those of H II regions in the discs of more massive spirals. This may be related to the absence of flattening of the gradients in the external parts of NGC 300 and M33. Finally, we find very similar N/H gradients in both galaxies and a fair correlation between the slope of the N/H gradient and MV comparing with similar data for a sample of spiral galaxies.