This work aims at designing a low-complexity precoding technique in the downlink of a large-scale multiple-input multiple-output (MIMO) system in which the base station (BS) is equipped with M antennas to serve K single-antenna user equipments. This is motivated by the high computational complexity required by the widely used zero-forcing or regularized zero-forcing precoding techniques, especially when K grows large. To reduce the computational burden, we adopt a precoding technique based on truncated polynomial expansion (TPE) and make use of the asymptotic analysis to compute the deterministic equivalents of its corresponding signal-to-interference-plus-noise ratios (SINRs) and transmit power. The asymptotic analysis is conducted in the regime in which M and K tend to infinity with the same pace under the assumption that imperfect channel state information is available at the BS. The results are then used to compute the TPE weights that minimize the asymptotic transmit power while meeting a set of target SINR constraints. Numerical simulations are used to validate the theoretical analysis.