Of course, Macedonia was also a rising power. But their invasion of Greece failed and only served to unite the Greeks against their outside enemies. Who knows, perhaps with Spartan losses in several wars, the balance of power is such that they are all too weak to stand against an invasion.
But Carthage was a traditional ally of the King of Epirus, who was also an ally of Sparta. The 'Mediterranean Three', as we call this little alliance in modern times, coordinated a strike on the Roman Republic when Pyrrhus attacked. While Sparta didn't do much in the way of military, they gave support to the Epirites and Carthaginians, which allowed the two do defeat the Romans and divide the land between them.
Now, if we take Sparta out of the equation, Epirus will likely not get the popular support it had and go on to lose its alliance with Carthage (or the alliance is never created in the first place) and then lose the Roman War.