Robertson provided 13 assists from left-back in all competitions last season, helping the Reds to a 98-point second-place finish in the Premier League and victory in Europe.
Speaking to The Telegraph, Robertson revealed his delight at his sides European conquest, saying: "Winning the final – that sense of achievement – sunk in quickly.
"But the magnitude of it probably won’t sink for a bit longer. It is a different feeling when people see you as a Champions League winner.
"No one can take it off us. It was just incredible. On that open-top bus with all your pals, seeing how happy everyone is; and then when the bus turned into that main street..."
The Scotland international went on to say how that experience has made him and the rest of the squad hungry for more success, adding: "Everyone was in awe of what we had witnessed and experienced.
"But there is also a feeling with everyone here of using that feeling, going through the streets of Liverpool with 800,000 people, seeing our captain lift that trophy. It is a feeling we want to carry over. We want more of that."
The Champions League victory came one year after the Reds had lost in the final of the same competition to Real Madrid, going down 3-1 in Kiev.
Robertson told how the players used that experience to inspire their performances the following season, as he said: "We were using the sense of heartbreak of losing the final to drive us forward. That meant at 89 or 90 minutes of every game we were still flying about."
For all their excellence, Liverpool were unable to end their long wait for a Premier League title, as they fell one point short of Manchester Citys tally of 98 points. Reflecting on this, the full-back said: "Look, Man City deserved to win the league.
"If you are asking me now would you take 97 points again this season I will say ‘yeah’. I just think it was a special season with two teams right at it. But we do not look back with disappointment.
"We take all the positives, especially with the Champions League trophy. Had we not won that, it would not have been a disaster, but it would have been hard to take having nothing. That is why we were so determined to get that trophy. And that is why we want more.”