The 71-year-old confirmed his decision on Wednesday morning, bringing to an end 26 years of astonishing success at Old Trafford.
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"The way he treated me was like a son and I'll never forget that moment.
"To play under such a man, he was so demanding. His standards were so high. Yeah, we had our ups and downs – he had a lot of ups and downs with most of the players in that 1992-93 season – but as far as just total respect, the man was immense. He got the best out of me as a player, that's for sure.
"When I was at Blackburn [as a manager] and things weren't going well, we played Manchester United at Old Trafford and I spent 15 or 20 minutes in his office.
"He said to me: 'The only advice I can give you is don't let players take the mickey out of you. Don't give them anything because, if you give them an inch, they'll take a mile. The higher you go, you've got to be really stern in that message'."
Speaking before the relevation of Sir Alex's retirement, former charge Beckham hailed the Scot as perhaps having made a greater difference to his side than any other coach.
The Paris Saint-Germain star opined: "The impact that he has with the team, the players and the fans ... I don't think there's anyone around in football that has had that impact, ever."