Actually, yes, since it was so clearly stated in the episode.
IMO that's one of the reasons why the Romulan War is still so interesting to fans compared to other, not shown ones (e.g. the first Cardassian war, or Tzenketi(sp?)).
There's actually a number of plausible explanations:
1) TOS implied it was less starships pummeling each other (that really only became the norm with DS9), and more like advanced civilisations hurling nuclear rockets from a far distance towards each other
2)
ENT gave the perfect explanation: Romulans used primarily drones. Nothing says the war was fought on equal footing (ships vs ships). Could have been "manned ships vs drone swarm" battles, with the few command ships going auto-destruct when defeated
3) NEM introduced the Remans. Totally possible the Romulans sent a bunch of warriors from subjugated races to the front. When humans checked the bodies on the battlefields, they might have found a large variety of dead aliens and assumed some of them to be Vulcans.
Totally off-topic by the way

I just love to speculate about this specific part of Trek lore, because it's so unique