An angular analysis of B0→J/ψK+π- decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3 fb-1 collected with the LHCb detector. The m(K+π-) spectrum is divided into fine bins. In each m(K+π-) bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by K∗ resonances is examined, making minimal assumptions about the K+π- system. The data reject the K∗-only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the m(J/ψπ-) vs m(K+π-) plane suggests structures near m(J/ψπ-)=4200 and 4600 MeV.