On the eve of the Champions League proper starting, Ronaldo finds himself aiming for a fourth successive title, having been a member of the Madrid team that won three in a row under Zinedine Zidane.
Over the summer, though, he traded the Spanish capital for Turin, where he turns out for Juventus.
Losing the five-time Ballon d’Or winner has not hurt Los Blancos, though, according to Alves.
"I think that, contrary to what everybody else says, Madrid are more of a team without Cristiano, and now it's a little more difficult than it was before - at least because of how I see football and my concept of this game,” he explained to Marca.
"Though it's obvious that him leaving is a brutal loss, Madrid are Madrid.”
The 35-year-old knows exactly why Ronaldo felt he needed to move on, though.
“People want challenges, to continue feeling alive and for that reason it doesn't surprise me,” he explained.
“He had been there for a while, he had done great things with Real Madrid and he has decided to try other things.
“I did when I was at Barcelona and the true fighters need new challenges and don't need comfort.
“I think that, like me at Barcelona, he was very comfortable and, maybe, we need something different to stimulate us again.”
Meanwhile, Dani Alves’ own ambitions see him aiming to win the title with PSG, who start their campaign against Liverpool at Anfield on Tuesday.
Although he is absent because of a long-term injury, he has a “good feeling” about the Ligue 1 champions’ prospects.
"To achieve the goal that this club wants is not so complicated,” he argued.
“But you need different things, to do different things, a different spirit, have a different mentality.
“This year I have a good feeling, things are improving here and they are doing well, there are things that are changing and people are understanding a bit of what this game is about.”
New head coach Thomas Tuchel could be the man to bring these ingredients to the squad, the Brazil international defender has said.
“He has an incredible spirit and has changed many things here regarding team spirit and mentality,” he added.
“We have a great challenge ahead against great rivals, but we accept it and prepare ourselves for it, knowing that in order to qualify we have to improve, for example, what we do in the French championship.”