In the seconds after collapse of a massive star, the newborn protoneutron star (PNS) radiates neutrinos of all flavours. The absorption of electron-type neutrinos below the radius of the stalled shockwave may drive explosions (the ‘neutrino mechanism’). Because the heating rate is proportional to the square of neutrino energy, flavour conversion of μ and τ neutrinos to electron-type neutrinos via collective neutrino oscillations (CνO) may in principle increase the heating rate and drive explosions. In order to assess the potential importance of CνO for the shock revival, we solve the steady-state boundary value problem of spherically symmetric accretion between the PNS surface (rν) and the shock (rS), including a scheme for flavour conversion via CνO. For a given rν, PNS mass (M), accretion rate () and assumed values of the neutrino energies from the PNS, we calculate the critical neutrino luminosity above which accretion is impossible and explosion results. We show that CνO can decrease the critical luminosity by a factor of at most ∼1.5, but only if the flavour conversion is fully completed inside rS and if there is no matter suppression. The magnitude of the effect depends on the model parameters (M, and rν) through the shock radius and the physical scale for flavour conversion. We quantify these dependencies and find that CνO could lower the critical luminosity only for small M and , and large rν. However, for these parameter values CνO are suppressed due to matter effects. By quantifying the importance of CνO and matter suppression at the critical neutrino luminosity for explosion, we show in agreement with previous studies that CνO are unlikely to affect the neutrino mechanism of core-collapse supernovae significantly.