It was Drogba's first game against Chelsea since he left in 2012 after helping the Blues beat Bayern Munich in the 2012 Champions League final.
The striker was well shackled by the Blues defence but still had his moments and threatened when his header flashed across goal and was volleyed against the post by Selcuk Inan.
He hopes to make more of an impact in the second leg and thinks Galatasaray can feel confident of making it through to the quarter-finals after an encouraging second half, when Aurelien Chedjou cancelled out Fernando Torres' ninth-minute opener.
"It was a special game, to play against my old team-mates," Drogba told Sky Sports.
"I didn't get a lot of chances but the header was perfect - well, not perfect because I didn't score, but it was a great cross, I wish I could have scored this one but there is another game.
"It was a great game and I think it is a good result.
"Chelsea are the better team on paper but second half we showed we can create them some problems. Now we have to go out and do it at Stamford Bridge.
"They played on the counter-attack and we were a bit naive two or three times. We know they are dangerous, we have to work on that and solve these problems.
"If we manage to score a goal there, it's a different game. One-one is a good result."