The 35-year-old moved to the Turkish side from Shanghai Shenhua during the winter transfer window, and he admitted that finances thwarted a return to his former club instead.
"It was not possible this winter," Drogba told Canal+. "Financially, there are ways to find solutions that make everyone happy, but it was complicated.
"There are supporters who still say that I went to China when I had said I would come back [to Marseille].
"It's a matter of what is feasible. And it was not feasible.
"So, what do I do? Waiting instead of continuing my career? Obviously, I continued, keeping my heart blue and white. It's simple."
Drogba played for Marseille for just a single season, during the 2003-2004 campaign, but helped the club to reach a UEFA Cup final, where it was beaten 2-0 by Valencia. Drogba is currently preparing for the UEFA Champions League quarterfinals where he will face his former manager at Chelsea, Jose Mourinho, when Galatasaray meets Real Madrid.