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The left-back, who was 20 at the time, played the entire 90 minutes as the Reds won 1-0 and progressed to the fifth round of the competition.
"Listen, it's every boys' dream playing for Liverpool, especially being a scouser and a Liverpool boy, growing up and being around it," Lewis told Liverpool Echo.
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"My whole family was there on that day.
It was a touch of class from the Scotland international, who has become synonymous to being a class act on and off the pitch.
"When I made my debut, he (Robertson) was the first person to message me, say well done and congratulated me because he did see how hard I was working for that," Lewis said.
The German gave him his first taste of senior football in training and then offered him opportunities in pre-season and on the competitive stage.
It may have not worked out in the end, but Lewis is thankful for everything Liverpool and Klopp did for him.
When asked about his time working under Klopp, Lewis said: "Listen, a man of that calibre you've got to trust what he says and everything he said was truthful.
Adam Lewis on his Liverpool debut in February 2020(Image: Getty Images)
"He told me I needed to get out on loan, get some game time, get around professional players and men, getting games under my belt.
Lewis is expected to compete with Lewis Gordon for the No.1 left-back spot this season.
"There is so much competition in this team," Lewis continued.
"We've got another left-back in Lewis Gordon who played a lot of games last year and we are different players.
"He is more of a defensive player, he is probably better defensively than me, but going forward I would fancy myself.