An angular analysis of $B^0to J/psi K^+pi^-$ decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3~${rm fb}^{-1}$ collected with the LHCb detector. The $m(K^+pi^-)$ spectrum is divided into fine bins. In each $m(K^+pi^-)$ bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by $K^ast$ resonances is examined, making minimal assumptions about the $K^+pi^-$ system. The data reject the $K^ast$-only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the $m(J/psipi^-)$ versus $m(K^+pi^-)$ plane suggests structures near $m(J/psipi^-)=4200$~MeV and 4600~MeV.