Partitioning of evapotranspiration and estimating of irrigation contribution to evaporation play a crucial role in managing scarce water resources and help in increasing the water productivity of crops, especially of sparsely vegetated plants. In this study, the FAO-56 dual crop coefficient (DCC) approach for estimating evaporation from soil under cropped conditions is adapted for subsurface drip irrigation (SDI). This new approach involves one additional variable, the fraction of the irrigation depth contributing to evaporation (fI,Es), which was defined and integrated into the FAO-56 equations for estimating daily water balance from the evaporation layer (0–15 cm). Impacts of soil texture, heterogeneity, irrigation depth, design parameters of the irrigation system on fI,Es, and the fraction of the soil surface wetted by irrigation (fw) (and consequently the exposed and wetted fraction (few)), were evaluated through HYDRUS-2D simulations. The modified procedure was compared with the existing FAO-56 method for estimating components of annual ET for wine grape under SDI. The model simulations showed that the fI,Es fraction in a homogeneous, isotropic light-textured soil was minimal (0.04) when SDI was placed at a depth of 25 cm. However, in medium and heavy textured soils fI,Es was 4 times larger than in light-textured soils. The value of fw was slightly higher in fine-textured (0.09) than in medium-textured soils (0.07). In Duplex soils with two contrasting textural layers, fw (0.12–0.16) was higher due to the presence of a heavy-textured soil layer just below the drip line. Similarly, in Triplex soils (3 different textural layers), placing the drip line in the middle layer effectively reduced both fI,Es and fw close to zero. In contrast, fw (0.18–0.30) and fI,Es (0.28–0.42) both increased considerably in heterogeneous soils. Both fractions (fw and fI,Es) increased with an increase in irrigation depths, except for fI,Es in loamy sand. The fractions were slightly lower when a drip line was placed at a depth of 10 cm (an evaporation zone) than when it was placed on the soil surface. Applying the same amount of water with different discharge rates had little impact on fI,Es and fw fractions. An increase in the drip line spacing proportionally decreased the wetted fraction on the soil surface. Annual evaporation for SDI irrigated wine grapes at the field study site, estimated using the existing FAO-56 procedure, was overestimated by about 5–6% compared to using the modified procedure. However, this deviation between the two approaches increased (18%) for heavier soil textures. It is concluded that the existing FAO-56 procedure needs to be adjusted when used to estimate evaporation under subsurface drip irrigation. However, the impact of the proposed modification on evaporation needs further evaluation under other crops, soils, and climatic conditions.