We investigate the precision with which the supernova neutrino spectra can be reconstructed in water Cherenkov detectors, in particular the large scale Hyper-Kamiokande and Super-Kamiokande. To this aim, we consider quasi-thermal neutrino spectra modified by the Mikheev-Smirnov-Wolfenstein effect for the case of normal ordering. We perform three 9 degrees of freedom likelihood analyses including first inverse-beta decay only, then the combination of inverse beta decay and elastic scattering on electrons and finally a third analysis that also includes neutral scattering neutrino-oxygen events. A tenth parameter is added in the analyses to account for the theoretical uncertainty on the neutral current neutrino-oxygen cross section. By assuming a 100% efficiency in Hyper-Kamiokande, we show that one can reconstruct the electron antineutrino average energy and pinching parameter with an accuracy of $sim2%$ and $sim7%$ percent respectively, while the antineutrino integrated luminosity can be pinned down at $sim3%$ percent level. As for the muon and tau neutrinos, the average energy and the integrated luminosity can be measured with $sim7%$ precision. These results represent a significant improvement with respect Super-Kamiokande, particularly for the pinching parameter defining the electron antineutrino spectra. As for electron neutrinos, the determination of the emission parameters requires the addition of supplementary detection channels.
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