Optical Kerr resonators support a variety of stable nonlinear phenomena in a simple and compact design. The generation of ultrashort pulses and frequency combs has been shown to benefit several applications, including spectroscopy and telecommunications. The most common anomalous dispersion Kerr resonators can be accurately described by a well-studied mean-field Lugiato-Lefever equation (LLE). Recently observed highly chirped pulses in normal dispersion resonators with a spectral filter, however, cannot. Here we examine the LLE in the normal dispersion regime modified with a Gaussian spectral filter (LLE-F). In addition to solutions associated with the LLE, we find stable highly chirped pulses. Solutions are strongly dependent on the filter bandwidth. Because of the large changes per round trip, the validity of the LLE-F fails over a large range of experimentally relevant parameters. While the mean-field approach leads to accurate predictions with respect to the nonlinearity coefficient and the dispersion, the dependence of drive power on loss deviates significantly from an experimentally accurate model, which leads to opportunities for Kerr resonators including frequency comb generation from low-Q-factor cavities.