It was announced last week that Robertson would leave when his deal expires at the end of June.
After victory over Fulham on Saturday, the Scotland left-back expanded on why he has decided to depart this summer.
"There have been discussions all season," Robertson said. "Last summer I was close to having a decision to make and I decided to stay. It was the same in January. It was more a discussion with the club and it was an open and honest conversation.
"I've always said I've had an amazing relationship with the owners and people like that. It was just a sit-down with my wife to see what we wanted next and obviously we'll see where we go, but it's important to end this story and we'll see whatever comes next.
"I want to play, so that was where the discussions came. It's not like I've knocked back a contract or anything, there was no contract on the table. It was a conversation we all had. It was a conversation of: 'Okay, this is what I want to do, I want to play and I believe I've still got the ability to play'. I think I have showed that this season.
"Look you can't be promised (starts) at this club - and that's absolutely fine. It can't be promised at any club. But it's also maybe time for the story to end and obviously me and Mo both made that decision this year.
"You're not getting any younger. I saw a picture the other day of the Champions League final and even from the big squad picture, there's only five or six of us left.
"Look, these eras come to an end. That's what's happening - and in the next couple of years some of the other lads will leave in terms of their contracts and things like that."