In a preliminary study, commercial insect powders were successfully identified using infrared spectroscopy combined with multivariate analysis. Nonetheless, it is necessary to check if this technology is capable of discriminating, predicting, and quantifying insect species once they are used as an ingredient in food products. The objective of this research was to study the potential of using attenuated total reflection Fourier transform mid-infrared spectroscopy (ATR-FTMIR) combined with multivariate analysis to discriminate doughs and 3D-printed baked snacks, enriched with Alphitobius diaperinus and Locusta migratoria powders. Several doughs were made with a variable amount of insect powder (0–13.9%) replacing the same amount of chickpea flour (46–32%). The spectral data were analyzed using soft independent modeling of class analogy (SIMCA) and partial least squares regression (PLSR) algorithms. SIMCA models successfully discriminated the insect species used to prepare the doughs and snacks. Discrimination was mainly associated with lipids, proteins, and chitin. PLSR models predicted the percentage of insect powder added to the dough and the snacks, with determination coefficients of 0.972, 0.979, and 0.994 and a standard error of prediction of 1.24, 1.08, and 1.90%, respectively. ATR-FTMIR combined with multivariate analysis has a high potential as a new tool in insect product authentication.