We prove that unary Sherali-Adams requires proofs of size n(Omega(d)) to rule out the existence of an n(Theta(1))-clique in Erdos-Renyi random graphs whose maximum clique is of size d <= 2 log n. This lower bound is tight up to the multiplicative constant in the exponent. We obtain this result by introducing a technique inspired by pseudo-calibration which may be of independent interest. The technique involves defining a measure on monomials that precisely captures the contribution of a monomial to a refutation. This measure intuitively captures progress and should have further applications in proof complexity.