The Croatian was signed from Tottenham Hotspur for €40m (£33m) this week, but the German international has said he is unconcerned by the added competition and thinks that a team like Madrid is always going to have great strength in depth.
"There is always a lot of competition when you play for a team like Real Madrid," admitted Ozil.
"We do not have just 11 players, but Madrid always have about 18 great players. You simply get used to that. It is not about Ozil, Modric or Kaka. The team is all that matters."
Ozil was signed from Werder Bremen in 2010.