Not quite so. Pyrric means you mean the battle but you lack the numbers to continue the campaign. Just like in Pyrro invasion of Italy.
Pyrrhos allegedly (
pace Ploutarchos, in his
Lives of the Famous Greeks and Romans) said of the Battle of Asculum, "One more such victory, and we are undone." Supposedly, the reason was precisely the one you're talking about: because he lost so many men there, he would not have the strength to continue the war.
The problem is that this is basically impossible. At Asculum, P. Decivs Mvs' Roman army of ~40,000 suffered twenty percent battle casualties and basically disintegrated in a rout afterwards. Meanwhile, Pyrrhos' own army, of similar size, endured seven percent casualties and was still quite combat effective; he used most of that army to invade Sicily the following year and roundly defeated the Qarthadastim. That's actually an extraordinarily lopsided victory in favor of Pyrrhos. It's virtually impossible to imagine a
more favorable outcome at Asculum for him.
There's basically no reason to believe that Ploutarchos' extremely late quote is anything more than apocryphal. Pyrrhos probably didn't continue his invasion of Rome for the same reason he failed to finish
literally anything else he ever did. He simply could not sit still and complete a task. He'd start something, then put off finishing it until later and go chase the latest shiny object. Eventually, in 272 BC, it killed him: he conquered most of Makedonia but failed to finish Antigonos Gonatas' forces off, then he invaded Sparte and couldn't finish the Lakedaimonians off, and then he attacked Argos and Antigonos' army caught up with him, and Pyrrhos died in the ensuing battle.
So, amusingly, the famous term "Pyrrhic victory" is not based on any reality at all. I agree with you: the modern usage of the term is "an extremely costly victory that ends up looking more like a defeat regardless of what happened on the battlefield". But that is not because Pyrrhos actually won any Pyrrhic victories. We can't appeal to Pyrrhos' own history to make the definition. It just is what it is: an eternal misnomer.