Recently, the LIGO observatory reported the first direct observation of gravitational waves, with a signal consistent with a binary black hole merger. This detection triggered several follow-up searches for coincident emission in electromagnetic waves as well as neutrinos, but no such emission was found. In this article, the implications of the nondetection of counterpart neutrinos are investigated using general arguments. The results are interpreted with a parameter denoting the energy emitted in neutrinos relative to the energy emitted in gravitational waves. The bound on this parameter from the diffuse astrophysical neutrino flux detected by the IceCube Neutrino Observatory is discussed. It is found that, currently, the nondetection of counterpart neutrinos puts a bound comparable to the one from the diffuse astrophysical neutrino flux. This bound is then used to constrain the amount of matter in the black hole binary environment. Finally, the sensitivity to this parameter in future gravitational wave observation runs is investigated. It is shown how the detection of one or more neutrinos from a single merger would strongly constrain the source population and evolution.