He began his farewell by playing the full 90 minutes as Liverpool beat Fulham 2-0 on Saturday.
The 32-year-old said: “Look, all good things come to an end. I’ve been here nine years and I couldn’t have dreamed of it being any better with all the trophies I’ve won.
“To stay at a club like this for nine years is something I’m incredibly proud of but it’s now time for me and my family to let Liverpool crack on and I’ll look back on some amazing memories.
“Obviously the announcement came this week. It means I don’t have to lie to everyone so it’s a weight off my shoulders.
“That was the main reason to do it, but now I am really focused on just trying to finish the season as strongly as possible because that’s what this club deserves from me.
“I’ve done that since day one and I won’t stop until I leave.”
Robertson, who was linked with Tottenham in January, is no longer an automatic choice at Liverpool but believes he still has plenty to offer.
He said: “It’s not like I’ve knocked back a contract or anything, there was no contract on the table.
“I want to play and I believe I’ve still got the ability to play.
“I will be looking to sort my future out sooner rather than later. I don’t want to be going to the World Cup with anything hanging over my head, so there will be conversations and things like that, but as of yet, there’s nothing.”