Miroslav Djukic's men had the perfect opportunity to win the game with Cartabia's spot-kick in the 17th minute, only the Argentine forward to have his effort from 12 yards saved.
Deportivo then played for over an hour with 10 men at the Estadio Municipal El Arcangel after Helder Postiga was shown a second yellow card, but Cordoba could not find the winning goal.
It means the Andalusia side remain the only team in La Liga without a win and they are bottom of the table with just six points from 11 matches.
The flash point of the match came in the 17th minute when Postiga was yellow carded for handball in the area.
But Cartabia's penalty was well saved by Fabricio to his right in the Deportivo goal.
Postiga then received his marching orders shortly before the half-hour mark for a second bookable offence.
Predictably Cordoba enjoyed most of the possession after the break but they were unable to find the breakthrough in a disappointing draw.