Former England international Scholes had brought an end to his playing days in the summer of 2011.
However, by the following January he had returned to the squad after admitting that he missed the game.
Discussing the reappearance of veteran Scholes, 19-year-old Pogba conceded that he was then aware that it was time to move on.
"When I saw Scholes come back part of me was really happy as he's a legend, but I knew it was the end for me. The manager thought Scholes had to play, not me, and after that I had to leave," he told The Times.
"It was all down to Ferguson. I didn't want to sign a contract as Ferguson didn't play me, even though there were no midfielders there. He obviously thought I didn't deserve the contract I asked for and didn't put me in the team even though he had no midfield players, it was his choice," he added.
"United were short of midfield players like me, but it was the manager's decision. I couldn't do anything about it. I was very frustrated because he spoke to me a few times and said I was nearly there.
"I told him: 'If I don't play, then I can't get any experience and see how far I have to go.' I played in a few cup games but he didn't want to give me a contract and they just let me go."
Pogba has made 21 appearances this season for Juve, scoring four goals.