A second-half penalty goal courtesy of Moussa Sow threatened to derail les Elephants' attempt to reach Brazil next summer, until Salomon Kalou's equaliser in the fourth minute of stoppage time ensured Sabri Lamouchi's side sealed their place.
"It will be the third World Cup in a row for a small country like Cote d'Ivoire. I am proud to be part of this adventure and then enter the history of football in my country with the third consecutive qualification," Drogba told reporters after the match.
"We're happy, we'll go home and enjoy this. We want to do something interesting at the World Cup. The previous two were difficult. Here we hope to have a few more chances and at least qualify from the first round."
The former Chelsea striker also took the time to praise the Senegal's efforts after a spirited performance in Morocco.
"Congratulations to Senegal that, despite the score, they never gave up hope and played bravely," he added.