In this paper we establish optimal convergence rates for solutions of equations describing unsteady, incompressible, shear-thickening fluid flow with homogeneous Dirichlet boundary conditions. We employ a semi-implicit full space-time discretization combining a backward Euler scheme in time with a Finite Element discretization in space and obtain the estimates without the use of intermediary semi-discrete problems. Our primary contribution is the proof of convergence rates for the shear-thickening case, a novel development within this specific context.