Romans didn't see Carthage as a barbarian country.

In the Aeneid, the poem by Virgil, the foundation of Rome is retold from a different point of view, trying to tie the lines between the fall of Troy and the travel of the hero Eneas that in the end gets to found Rome and find his foretold destiny.

During the middle of the travel, the goddess Juno, aided by Venus and Cupid suceed in making Eneas stray and wash ashore Carthage, where the queen Dido falls in love with him. Afterwars, as Eneas leaves Carthage to fulfill his destiny, Dido kills herself.

Just as the Homeric saga present the rapture of Helen of Troy as the reason for the war between Greeks and Troyans, Virgil present the rivalry between Rome and Carthage as being caused by Dido's suicide.

According to this interpretation, Carthage and Rome are sister cities, divided just because a love affair which in turn was caused by the gods and their trickery.

Mago was a Carthaginian agricultural writer whose works were preserved at the sack of Carthage and translated into Latin and Greek. Later Roman agricultural writers heavily drew upon him.

Beyond that, as others say here, the Romans didn't really demonize the Carthaginians as being uncivilized. Tricky, dishonest and greedy, yes, but they were fully aware of their cultural achievements.

Publius Cornelius Scipio Nasica Corculum argued against a third war with Carthage because he thought that Carthage keep coming back from the dead kept Rome on her toes and would lead to the decline of Roman morals and discipline.