The COHERENT experiment has detected the coherent elastic neutrino-nucleus scattering for the first time, and its measurement is consistent with the standard model (SM) prediction. We present a simple calculation of the detected spectrum, and use it to put constraints on the nonstandard neutrino interactions (NSI). For NSI generated by a very light mediator, only couplings of the mediator are constrained by the COHERENT data, and large NSI are still viable. For a heavy mediator, despite the fact that constraints are severely weakened by the degeneracies between the NSI parameters, current COHERENT data can place meaningful constraints on the effective NSI parameters in Earth matter.