<p>In this paper, the authors consider the non-relativistic limit of solutions to the defocusing cubic nonlinear Klein-Gordon equations. Inspired by the work of Lei and Wu (2023), which considered the real-valued case, the authors show that the solutions to the complex Klein-Gordon equation can be described by using a system of two coupled nonlinear Schrödinger equations as the speed of light tends to infinity both in two and three dimensions. On the one hand, if the initial data belong to a lower-regularity Sobolev space <i>H</i>^<i>α</i>, <i>α</i> ∈ [1, 4], the error is proportionate to the <i>α</i> order of the reciprocal of the speed of light, with a constant that grows linearly in time. On the other hand, if initial data are smoother (at least in <i>H</i>⁴), the error is proportionate to the square of the reciprocal of the speed of light, with a constant that grows linearly in time. The error of two different regularity requirements holds globally over time.</p>