The full-back has lost his place in the Reds XI to Kostas Tsimikas at times this season after struggling for form but is still determined to play an important role for Arne Slot's team.
Robertson - who returned to the team as Liverpool beat Aston Villa at the weekend - said: "Last couple of games I've been on the bench and I got doubters for the first time in a long time, first time at this club. But it suits me in this position. I am trying to prove people wrong again. I tried to do that against Villa.
"I want to play every game, of course, but that was not possible. I knew that the next time I got a chance I would take it and that's what I tried to do."
Robertson was a fixture in the Liverpool team under former boss Jurgen Klopp and believes that he can be vital for the club under Slot's leadership.
The Scotland captain said: "Look, I am a lot older and a lot wiser now than when I came in. When I first came in I was only 23, first time playing for a big club. I have been here for seven years and won everything, played in a lot of big games.
"I am a lot more experienced and a lot better at switching off from everything like overreactions and things like that. Probably a bad 45 minutes of football against Arsenal (last month), it was not great. I think pretty much everyone had written me off after that. That is football and that is what happens these days.
"People can write me off all they want. But I will always try to keep working, keep improving. I have tried to do that and hopefully I have shown that."