Background and Objectives: Dual antiplatelet therapy (DAPT) is essential in the treatment of patients with acute coronary syndrome (ACS). The objective of this study was to evaluate the effectiveness of antiplatelet medication in our practice and to investigate the factors that influence it. Materials and Methods: A prospective cohort observational study was conducted, in which 193 patients with ACS were enrolled. The patients were stented in the catheterization laboratory between May 2019 and October 2020, before and during the COVID-19 pandemic, and were receiving DAPT. Their platelet functions were tested using a Multiplate Analyzer. In addition to this, clinical data, demographics, laboratory tests, and cardiovascular risk factors were also analyzed. Results: 43.46% of the patients treated with aspirin were found to be resistant to it. This phenomenon was more common in men (48.17% vs. 31.48%, p = 0.036), and it was associated with being under the age of 50 (OR: 2.08; 95% CI: 1.11–3.90) and weighing over 70 kg (OR: 3.00; 95% CI: 1.21–7.40). Most of the patients treated with clopidogrel were in the optimal treatment window, while about half of the patients treated with ticagrelor had an exaggerated pharmacological response. Among the laboratory parameters, leukocytosis and platelet count were found to be determinants of platelet reactivity for both the aspirin and ticagrelor treatments. Conclusions: Many patients treated with antiplatelet agents are outside of the treatment window. The results obtained showed that low doses of gastro-resistant aspirin tablets are ineffective, and their efficacy can be influenced by various clinical and laboratory factors. Patients receiving ticagrelor have significantly reduced platelet reactivity, influenced only by certain laboratory indicators. The pandemic significantly influenced the results of the platelet aggregation tests only in patients treated with clopidogrel.