Optical Kerr frequency combs (KFCs) are an increasingly important optical metrology tool with applications ranging from ultraprecise spectroscopy to time keeping. KFCs may be generated in compact resonators with extremely high quality factors. Here, we show that the same features that lead to high quality frequency combs in these resonators also lead to an enhancement of nonlinear emissions that may be identified as originating from the presence of a negative frequency (NF) component in the optical spectrum. While the negative frequency component of the spectrum is naturally always present in the real-valued optical field, it is not included in the principal theoretical model used to model nonlinear cavities, i.e., the Lugiato-Lefever equation. We therefore extend these equations in order to include the contribution of NF components and show that the predicted emissions may be studied analytically, in excellent agreement with full numerical simulations. These results are of importance for a variety of fields, such as Bose-Einstein condensates, mode-locked lasers, nonlinear plasmonics, and polaritonics.