The 20-year-old, who joined the Tigers from Dundee United for £2.85million, says his height was behind Celtic's decision to release him as a 15-year-old.
"That was the reason given but I took it on the chin and bounced back," said Robertson.
And when asked if that made him more motivated, he said: "Yeah, in a way."
Robertson moved to Queen's Park following his exit from Parkhead. He broke into the first team and after a season was snapped up by Dundee United, where he spent one season.
"Going down to Queen's Park, some people would have thought it was a strange move," he added.
"But I can't thank them enough for what they did for me over four years. They helped make me the player I am. At United the manager and players were brilliant."
After revealing his delight at sealing a switch to Steve Bruce's Hull side, Robertson insisted he is not daunted by the prospect of playing in the English top flight.
"I went from the Third Division to the Scottish Premier League, which is a big step. I know this is going to be bigger, but I feel I've got the ability to deal with it," he added.
"The short term goal is to try to break into the team and cement my place in the starting 11.
"I'm really looking forward to getting started now, meeting the boys and getting on the training field.
"As soon as I spoke to Steve Bruce he was very welcoming and said all the right things. I'm really looking forward to working under him."