The Higgs-dilaton cosmological model is able to describe simultaneously an inflationary expansion in the early Universe and a dark energy dominated stage responsible for the present day acceleration. It also leads to a nontrivial relation between the spectral tilt of scalar perturbations n(s) and the dark energy equation of state omega. We study the self-consistency of this model from an effective field theory point of view. Taking into account the influence of the dynamical background fields, we determine the effective cutoff of the theory, which turns out to be parametrically larger than all the relevant energy scales from inflation to the present epoch. We finally formulate the set of assumptions needed to estimate the amplitude of the quantum corrections in a systematic way and show that the connection between n(s) and omega remains unaltered if these assumptions are satisfied.