Beckham appears in the Class of '92 documentary, which reflects on the club's FA Youth Cup winners 21 years ago.
Ryan Giggs, Paul Scholes, Gary Neville and Nicky Butt were Beckham's teammates, but their talent did not earn them favourable treatment from Ferguson.
The Class of '92 (and Phil Neville), reunited in 2011
"Not in a bad way but we were all very scared of him," Beckham said.
The former England captain recalled how all five players, as well as Class of '95 captain Phil Neville, moved through the ranks from the youth team through to first team plus national level and "did it as friends".
He said: "We did it and won everything in football - it does not get any better than that."
The film covers the period from 1992 to 1999, culminating in the club's Champions League triumph.
Beckham, 38, predicted an announcement about whether he would be in charge of a US soccer team would be "at some point before the new year" but he said that he would not be a manager.