The former Barcelona striker has struck twice, including the equaliser at Real Valladolid on Sunday, and told AS: "As much my as the team's beginning has been very good.
"Everyone talks about Madrid not playing as a team, but we have had to in the last two games against Valladolid and Almeria, both which made it very difficult for us.
"I know I cannot demand a start in this team. Nobody has a guaranteed position. (Coach Bernd) Schuster has already told us we all will play many games this season, not because it's his policy, but because we have a very heavy programme."
Asked about criticism from Barca president Joan Laporta, Saviola added: "Laporta's comments surprised me a lot because I thought I had a warm relationship with him and the directors. I had hoped he wouldn't have said such things.
"Laporta attacked me without any reason."