Recently we identified cycloguanil-like dihydrotriazine derivatives, which provided host-factor directed antiviral activity against influenza viruses and respiratory syncytial virus (RSV), by targeting the human dihydrofolate reductase (hDHFR) enzyme. In this context we deemed interesting to further investigate the structure activity relationship (SAR) of our first series of cycloguanil-like dihydrotriazines, designing two novel azaspiro dihydrotriazine scaffolds. The present study allowed the exploration of the potential chemical space, around these new scaffolds, that are well tolerated for maintaining the antiviral effect by means of interaction with the hDHFR enzyme. The new derivatives confirmed their inhibitory profile against influenza viruses, especially type B. In particular, the two best compounds shared potent antiviral activity (4: EC50 = 0.29 μM; 6: EC50 = 0.19 μM), which was comparable to that of zanamivir (EC50 = 0.14 μM), and better than that of ribavirin (EC50 = 3.2 μM). In addition, these two compounds proved to be also effective against RSV (4: EC50 = 0.40 μM, SI ≥ 250; 6: EC50 = 1.8 μM, SI ≥ 56), surpassing the potency and selectivity index (SI) of ribavirin (EC50 = 5.8 μM, SI > 43). By a perspective of these results, the above adequately substituted azaspiro dihydrotriazines may represent valuable hit compounds worthy of further structural optimization to develop improved host DHFR-directed antiviral agents.