We study the inverse proximity effect in a bilayer consisting of a thin s-or d-wave superconductor (S) and a topological insulator (TI). Integrating out the topological fermions of the TI, we find that spin-orbit coupling is induced in the S, which leads to spin-triplet p-wave (f -wave) correlations in the anomalous Green's function for an s-wave (d-wave) superconductor. Solving the self-consistency equation for the superconducting order parameter, we find that the inverse proximity effect can be strong for parameters for which the Fermi momenta of the S and TI coincide. The suppression of the gap is approximately proportional to e −1/λ , where λ is the dimensionless superconducting coupling constant. This is consistent with the fact that a higher λ gives a more robust superconducting state. For an s-wave S, the interval of TI chemical potentials for which the suppression of the gap is strong is centered at µTI = ± 2mv 2 F µ, and increases quadratically with the hopping parameter t. Since the S chemical potential µ typically is high for conventional superconductors, the inverse proximity effect is negligible except for t above a critical value. For sufficiently low t, however, the inverse proximity effect is negligible, in agreement with what has thus far been assumed in most works studying the proximity effect in S-TI structures. In superconductors with low Fermi energies, such as high-Tc cuprates with d-wave symmetry, we again find a suppression of the order parameter. However, since µ is much smaller in this case, a strong inverse proximity effect can occur at µTI = 0 for much lower values of t. Moreover, the onset of a strong inverse proximity effect is preceded by an increase in the order parameter, allowing the gap to be tuned by several orders of magnitude by small variations in µTI. arXiv:1808.03650v3 [cond-mat.supr-con]