Cavani had a productive first season with United, scoring 17 goals in 39 games.
However, he had to give up his no.7 shirt and starting spot to Ronaldo, who was signed late the following summer.
"At the moment it was done, I thought it was a good thing for Manchester to sign Cristiano," Cavani, now with Valencia, told ESPN Brasil.
"Knowing a bit about the world of football these days, the first thing I did was call my brother [Walter Fernando Guglielmone, who also acts as his agent] and said: 'Fernando, if this had happened a week ago, I would ask you to find me another club.'
"But not because I didn't want to play with Cristiano Ronaldo. No. Because I had the opportunity to know him, and he is a great professional, with his targets, and that is perfect for a sportsman.
"But as I know, after years in football, how things work these days. That's why I spoke to my brother.
"It was more about understanding the situation. Not because I couldn't play in my role at Manchester, but because there are many things in football nowadays that are different from how they were with other people, how it was before, years ago. And since it happened suddenly, I felt nothing. I thought: We'll play, do the best we can."