Well, what little we know about Carthaginian innovations (I assume you mean technological) comes from Roman sources written long after the destruction of Carthage, by which point the Romans had already adopted said innovations. Also keep in mind that Punic civilization didn't disappear overnight and lived on in Roman North Africa, more or less, until sometime after the Vandals invasion.

As for the innovations themselves, Varro refers to a threshing machine known simply as the plostellum Punicum or "Punic cart" (De Re Rustica 1.52.1). Carthaginian agricultural techniques in general received high praise in antiquity, and the Roman Senate even commissioned a translation of a Carthaginian handbook on farming (none of the original is extant, unfortunately). Various sources also mention pavimentum Punicum or "Punic pavement," which is apparently some type of flooring mosaic, though I suspect in the back of my mind that it may simply be another name for Numidian marble. The fermented (and no doubt smelly!) fish sauce garum evidently has Phoenician origins too; it may have been popularized by the Carthaginians. In addition, I recently encountered the term opus Africanum in scholarly literature, a modern term for Carthaginian masonry techniques.

For something a little more "innovative," the Marsala shipwreck revealed that the Carthaginians assembled their vessels using prefabricated and probably mass-produced parts (each component was numbered with an alphabetic construction mark). This might explain how the Romans, using a captured Carthaginian ship as a model, were able to churn out a hundred quinqueremes in sixty days at the start of the First Punic War. As far I am aware, however, there's no explicit evidence that anyone else in antiquity employed this method of shipbuilding.

That's all I remember for now. I hope you find this helpful! :D