Cosmic‐ray energy densities in central regions of starburst galaxies, as inferred from radio and γ‐ray measurements of, respectively, non‐thermal synchrotron and π0‐decay emission, are typically , i.e. typically at least an order of magnitude larger than near the Galactic Centre and in other not‐very‐actively star‐forming galaxies. We first show that these very different energy density levels reflect a similar disparity in the respective supernova (SN) rates in the two environments, which is not unexpected given the SN origin of (Galactic) energetic particles. As a consequence of this correspondence, we then demonstrate that there is partial quantitative evidence that the stellar initial mass function (IMF) in starburst nuclei has a low‐mass truncation at ∼2 M⊙, as predicted by theoretical models of turbulent media, in contrast with the much smaller value of 0.1 M⊙ that characterizes the low‐mass cut‐off of the stellar IMF in ‘normal’ galactic environments.