We utilize a recent formulation to compute the deflection angle of a light ray, namely, the Gauss-Bonnet theorem (GBT) to explore the semiclassical gravitational effects in the spacetime of a point-like global monopole and a cosmic string. Previously the Gauss-Bonnet theorem [Class. Quant. Grav. 25, 235009 (2008)] was proposed as an alternative way of compute the deflection angle of light. In the present article we have used the celebrated GBT that applied to the optical metric as well as the geodesic method in computing the deflection angle. For an important observation, when we modify the domain of integration we found an exact result between GBT and the standard approach up to the third-order contributions terms for the cosmic string and global monopole deflection angles, receptively.