Massive stars are the main objects that illuminate HII regions and they evolve quickly to end their lives in core-collapse supernovae (CCSNe). Thus, it is important to investigate the association between CCSNe and HII regions. In this paper, we present emission-line diagnostics of the stellar populations around nearby CCSNe, which include their host HII regions, from the Potsdam Multi-Aperture Spectrophotometer (PMAS)/PPak integral-field supernova hosts compilation (PISCO). We then use bpass stellar population models to determine the age, metallicity and gas parameters for HII regions associated with CCSNe, contrasting models that either consider single-star evolution alone or incorporate interacting binaries. We find that binary-star models, which allow for ionizing photon loss, provide a more realistic fit to the observed CCSN hosts, with metallicities that are closer to those derived from the oxygen abundance in O3N2. We also find that Type II and Type Ibc SNe arise from progenitor stars of similar age, mostly from 7 to 45Myr, which corresponds to stars with masses =<20M_{sun}_. However, these two types of SNe have little variations in their host environment metallicity measured by oxygen abundance or in progenitor initial mass. We note that at lower metallicities the SNe are more likely to be Type II.