Di Stefano died on Monday afternoon after suffering a heart attack on Saturday, the day after he turned 88, resulting in him being placed in an induced coma.
Among the many tributes, Madrid forward Cristiano Ronaldo hailed Di Stefano as a "maestro" while FIFA president Sepp Blatter described the Argentina-born forward as "the most complete player".
Di Stefano won five successive European Cups at Real Madrid between 1956 and 1960, scoring in all five fixtures - including a hat-trick in front of a watching Ferguson at Hampden Park in 1960.
He sits second on Real Madrid's all-time goalscoring list behind Raul and was an honorary president at the Bernabeu, with Ferguson ranking him among the very best.
"The great question that always comes up is who are the greatest players," Ferguson said in an exclusive interview with Sky Sports News.
"Obviously there is a list of great ones like (Johan) Cruyff, (Diego) Maradona and Pele and of course (Ferenc) Puskas and of course Di Stefano - I thought he was one of the greatest in my mind.
"He had a fantastic balance and poise. If you look at one of the goals he scored in the final against Eintracht Frankfurt it was completely what we are saying about the balance and poise, unbelievable he was.
"I was very sad to hear the news. Even at 88 it is a bit of a shock. I saw him two years ago before our Real Madrid game and he looked fine and looked full of health, so it is disappointing to hear the news."
An abiding memory for Ferguson was being in attendance as Di Stefano put Frankfurt to the sword in a 7-3 drubbing that ensured a fifth straight European Cup.
"The amazing thing about that was, being a Rangers fan, Eintracht Frankfurt had beaten Rangers in the semi-finals 6-3, 6-1 so they were gods," he said.
"They came to Hampden Park and were annihilated by Real Madrid 7-3. I was there in the schoolboy enclosure, I was playing with Queen's Park at the time, and it was a fantastic experience.
"It was the first time I think that a lap of honour was done after the game, Scottish fans hadn't seen that of course.
"Ten goals in a final, you won't see that again. It was a golden period for Real Madrid, they won it five times in a row and Di Stefano scored in all five finals."
The two would cross paths 23 years later when Ferguson, then manager of Aberdeen, met a Real Madrid side managed by Di Stefano in the 1983 Cup Winners' Cup final.
Against the odds it was Ferguson's Scottish underdogs who won the trophy that night, with the Glaswegian impressed by Di Stefano's grace in defeat.
"My greatest memory of course is when Aberdeen beat Real Madrid," he added.
"I was honoured to be in the same game as Real Madrid but to come up against Di Stefano was an incredible experience for me.
"When you mention the great players they had they were household names. Aberdeen were a team on the rise and after the game he was very generous and he said Aberdeen had a team that money can't buy, a soul and a family spirit.
"He couldn't say any more in praise of a football team and that was very generous of him. He had a fantastic life and I was really proud to have been associated with him in a small way."
Tributes continued to pour in elsewhere, with a number of former greats taking to social media to express their sadness at Di Stefano's passing.
Former Brazil great Pele on Twitter
"Today the openness between Latin American players and European clubs is very much due to the work of Alfredo Di Stefano. He was a trailblazer, and most of all, he was a legend of the game. God rest his soul."
Triple European champions Manchester United on Twitter
"We're sad to hear #RealMadrid legend Alfredo Di Stefano has passed away. The thoughts of everybody at #mufc are with his family & the club."
Former Italy defender Franco Baresi on Twitter
"It's a sad day. I want to remember Alfredo Di Stefano, one of the best players ever."
Ghana midfielder Michael Essien on Twitter
"RIP the great Alfredo Di Stefano. You will be missed in Madrid and all over the world."
Former Brazil defender Cafu on Twitter
"My condolences to the Di Stefano family, a great player whose name will remain in the world's football history."
Chelsea manager Jose Mourinho, formerly of Real Madrid, on the London club's website
"This is a very sad day for football ... when we lose a special person like this. Alfredo was the best Real Madrid player in history."
Former England and Manchester United midfielder Bobby Charlton on the club website
"The footballing world has lost a great player and a great man ... I had never seen such a complete footballer."
Spain midfielder Juan Mata
"RIP Alfredo di Stéfano. One of the greatest has passed away. My condolences to his family and friends."
Former England striker Michael Owen
"Saddened to hear that the Real Madrid legend Alfredo Di Stefano passed away earlier today. R.I.P.
Former England striker Gary Lineker
"Alfredo Di Stefano has died. One of the greatest players ever. Scored in 5 successive European Cup finals. A feat never to be matched
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