Antihistamine and Drowsiness. The most common side effect of an antihistamine is drowsiness. Antihistamines such as diphenhydramine and chlorpheniramine are more likely to cause drowsiness than any of the newer antihistamines available. This unwanted side effect of drowsiness occurs less frequently with the newer antihistamines such as citrizine, desloratadine, fexofenadine and loradtadine.