The Frenchman is not expected to play again until the New Year after breaking his foot in the Gunners' 2-2 draw with Everton last month.
"Olivier is an important player for us," Koscielny told Arsenal Player. "He's very strong during the game and he's scored a lot of goals. So for us it's very difficult to lose him, but I know him and I know he will come back stronger.
"He will want to show everyone that he can be a very good player and a good striker in the Premier League and in Europe. It is important for us that Olivier keeps this mentality and comes back stronger for us."
Following the injury blow to Giroud, Arsenal bought Manchester United striker Danny Welbeck for a reported £16m fee on transfer deadline day last Monday.