Ferguson, Beckham's manager of 10 years at Manchester United, writes in his autobiography Beckham is the "only player he managed who chose to be famous".
"When Beckham moved to America to join LA Galaxy, I believe he began to realise he had surrendered a part of his career," Ferguson says.
"I imagine he had his eyes on Hollywood and the impact it would have on the next phase of his career. There was no footballing reason for him to go to America.
"I like David. I think he's a wonderful boy. But you should never surrender what you're good at.
"David was the only player I managed who chose to be famous, who made it his mission to be known outside the game.
"In his final season with us, we were aware that David's work-rate was dropping. His application had dropped from its traditionally stratospheric level."
Beckham's last campaign at United was marred by an incident after their FA Cup 5th round loss to Arsenal. Ferguson was furious Beckham had failed to track Sylvain Wiltord for Arsenal's second goal, and accidentally kicked a boot at the midfielder after the match, cutting his eyebrow.
"Of course he rose to have a go at me and the players stopped him. 'Sit down,' I said. 'You've let your team down. You can argue as much as you like.'
"I called him in the next day to go through the video and he still would not accept his mistake. As he sat listening to me, he didn't say a word. Not a word.
"The next day the story was in the press. In public an Alice band highlighted the damage inflicted by the boot. It was in those days that I told the board David had to go."