The midfielder claims the team are not immersed in the desire to win titles next season, while he also praised recent signing Fabio Coentrao
The Spanish giants endured a frustrating campaign last season as they fell short of Barcelona in La Liga and in the Champions League, with their only consolation coming in the form of the Copa del Rey.
Madrid have since spent over €50 million [£43.8m] to bolster their squad and turn things around, and despite the pressure to deliver, Xabi Alonso refused to tell whether a season without titles would be a failure.
"It is always about improving and making progress. This is the second year of the project and that gives us continuity," he said at a press conference.
"We know each other better, the idea is there, now we just have to improve. We do not have to be obsessed, the best thing is that titles come naturally."
Fabio Coentrao, who cost Real Madrid €30m [£26.3m] to sign from Bendica this summer, has been tested in the midfield, and Xabi Alonso was impressed with the Portuguese's skills.
"He has made a very good impression, we knew he could bring a lot of good things," Alonso noted.
"He is a very complete player, he has a very good working pace. He can occupy several positions and that influenced his signing, so the impression is very good."