A series of 2,4-disubstituted pyrrolo[2,1-f][1,2,4]triazines containing both aryl and thienyl substituents were synthesized by exploiting the 1,3-cycloaddition reaction of N(1)-ethyl-1,2,4-triazinium tetrafluoroborates with dimethyl acetylenedicarboxylate. The antiviral activity of the synthesized compounds against influenza virus strain A/Puerto Rico/8/34 (H1N1) was studied in experiments on Madin-Darby canine kidney (MDCK) cell culture. Among the pyrrolo[2,1-f][1,2,4]triazine derivatives, compounds with low toxicity and high antiviral activity were identified. Dimethyl 4-(4-methoxyphenyl)-7-methyl-2-p-tolylpyrrolo[2,1-f][1,2,4]triazine-5,6-dicarboxylate was found to demonstrate the best antiviral activity (IC₅₀ 4 µg/mL and selectivity index 188). Based on the results of in vitro tests and molecular docking studies performed, a plausible mechanism of action for these compounds was suggested to involve inhibition of neuraminidase.