The Scotland international went on to play for Queen's Park and Dundee United before earning the move to Hull City in England in 2014.
Robertson joined Liverpool from Hull earlier this month for a transfer fee reported by The Telegraph to be worth £10 million.
The young defender has opened up on his departure from Scottish giants Celtic back when he was a teenager.
“There was a transition going on at Celtic at the time where a new head of youth had come in,” Robertson told The Telegraph. “I didn’t fit the bill.
“He came from Motherwell, who were full of big lads and were physical. That wasn’t my game. I was small. I’m not big now but it took me time to grow and fill out.
“He saw a small guy playing centre-mid, left-mid or left-back who was quite weak. To be fair I was, but I believed in my ability.
“That was the first time I had anyone doubt me. Tommy Burns [the former Celtic manager and head of youth development] was great with me and when he died it hit everyone hard.
“He was different class with me, he liked me as a player, he liked me as a person and he could see what potential I had.
“He sadly passed away and Celtic went another route afterwards, one which was hard on some players, but good for others that maybe didn’t fit Tommy’s vision.”
Robertson is a very good left-back, and the Scotsman could prove to be a brilliant signing for Liverpool.
Jurgen Klopp’s side needed an established left-back, as it would not have wise to have expected James Milner, who is a midfielder by trade, to have done the job yet again next season.