As a consequence of alcoholic fermentation (AF) in wine, several compounds are released by yeasts, and some of them are linked to the general quality and mouthfeel perceptions in wine. However, others, such as succinic acid, act as inhibitors, mainly of malolactic fermentation. Succinic acid is produced by non-Saccharomyces and Saccharomyces yeasts during the initial stages of AF, and the presence of some amino acids such as γ-aminobutyric acid (GABA) and glutamic acid can increase the concentration of succinic acid. However, the influence of these amino acids on succinic acid production has been studied very little to date. In this work, we studied the production of succinic acid by different strains of non-Saccharomyces and Saccharomyces yeasts during AF in synthetic must, and the influence of the addition of GABA or glutamic acid or a combination of both. The results showed that succinic acid can be produced by non-Saccharomyces yeasts with values in the range of 0.2–0.4 g/L. Moreover, the addition of GABA or glutamic acid can increase the concentration of succinic acid produced by some strains to almost 100 mg/L more than the control, while other strains produce less. Consequently, higher succinic acid production by non-Saccharomyces yeast in coinoculated fermentations with S. cerevisiae strains could represent a risk of inhibiting Oenococcus oeni and therefore the MLF.