Although it will not affect their Champions League campaign, Grant is set to lose Drogba as well as Salomon Kalou, Michael Essien and Mikel John Obi during the African Nations Cup in January.
Grant said: "Didier is a very good striker. Even though we win without him, we miss him and want him to play.
"But it is much more easier for him when we play and pass the ball well and create chances. He knows how to score.
"I have two months until he goes. Four of our very important players will not be in the squad for a long time. It is not easy but we cannot change it. We will have to do our best.
"We played some good football tonight and scored four goals. We had a lot of chances but what is most important is that we qualified for the next round one game before the end and after having dropped two points in the opening round.
"We want to play positive, attacking football and I am very happy with what has happened. We win games, we progress and play better from game to game.
"We are in the next round and in a good position in the league at home. I hope we can continue the process.
"It is a long way until May but Chelsea have never been in the final and this is one of our targets, maybe the main one, because we want to be a big club.
"We want to get to the final and I hope it is this year."