The German international moved to the North London club on the final day of the transfer window in a deal worth a reported £45m.
Courtois, who is on loan at Atletico from Chelsea, believes that the sale of Ozil will be a big loss for Carlo Ancelotti's team.
"Without Ozil, Madrid lack a certain quality in their game," Courtois told AS.
"Ozil had tremendous vision in playing the final pass between the lines and opening up the game, although it is true that they have others."
Ozil has made a fine start to his Arsenal career, assisting four goals in his first two Premier League games.