Ferguson claimed that he sold Beckham to Real Madrid in 2003 because the ex-winger had too big an ego.
However, Beckham has chosen to thank the Scot for giving him the opportunity to play for United instead of becoming embroiled in a war of words.
"I'm not going to sit here and be negative about a man who gave me the chance to play for my boyhood team," he said at a Facebook Live book signing.
"For me, like I said, he gave me the chance to do that. He believed in me, he believed in the rest of the young lads that came through with us."
Beckham spent 10 years as a player at Old Trafford before joining Madrid.