Saul admits the key reason was the lack of confidence he sensed from both the coaching staff and the Atleti support.
The midfielder spent last season on-loan with Sevilla before leaving Atletico.
He told RTVE: "I think it wasn't just the coaching staff anymore; I think some of the fans already saw me differently. I don't know if it was because of expectations or whatever, but they were never satisfied with what I was doing.
"Logically, I knew I could give much more, and we all knew it, but I think they saw me differently. They saw me differently, so I think I said, well, if a large part of them don't want me here, I don't want to hurt Atlético de Madrid either.
"If they don't want me, well, I know I have to move on and wish them the best. If that's how they see it, it's what I have to accept."
Saul added, "I'm always grateful to the fans, who have always supported me through thick and thin. And of course I miss Atlético de Madrid a lot."