"Of course we want to win but 15 other teams want to win as well," Drogba told reporters at the Royal Bafokeng Sports Palace.
"It's going to be hard, like today. It was very difficult and all we can do is give our best."
For a fifth successive tournament, the Ivorians are favourites to win the title but they have failed on their four previous attempts.
"People want us to win all the games, but it's not possible," Drogba said. "This is football after all."
Drogba said Ivory Coast, Africa's top-ranked team, did not under-estimate their opponents from west Africa.
"It was a tough game but we expected that," he said. "Togo gave us a good fight but we've also made a lot of mistakes and this is something I hope we can change in the next games.
"Still, 2-1 for us is a great win even if it was difficult," said Drogba who was substituted around 15 minutes from time after a subdued performance.
Midfielder Yaya Toure struck early for Ivory Coast but they had to wait for a goal from forward Gervinho to seal victory two minutes from time.
Ivory Coast face Algeria and Tunisia in their remaining group games.
The Elephants have twice been Africa Cup of Nations runners-up in the last four tournaments, were semi-finalists in 2008 and were knocked out in the last eight in 2010.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1