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."
Madrid beat United in the European Cup semi-finals in 1957 and Sir Bobby Charlton, who was on the losing side in the tie, echoed Ferguson's sentiments.
"As one of the stars of the legendary Real Madrid team, I think Alfredo was one of the best players I ever came across and an extremely intelligent footballer," Charlton told manutd.com
"He was somebody I really respected, having watched him from the stands at the Bernabeu and then played against him
I have many fond memories of my time with Alfredo and feel privileged to be able to call him a good friend
The footballing world has lost a great player and a great man ."
Chelsea boss Jose Mourinho led Madrid to their last Primera Division title and also paid his respects to Di Stefano on the Blues' website.
"It was with immense sadness I learned of the death of Alfredo Di Stefano, a wonderful man I had the fortune to know during my time in Madrid," he said.
"Alfredo was the best Real Madrid player in history - winning five consecutive European Cups - and one of the greatest of all time
Rest in peace Alfredo."
One of Real's current stars also offered his condolences as Ronaldo posted a tribute on Twitter.
"It's a very sad day
For me, for all the madridistas, for the world of football," he wrote
"Don Alfredo leaves us, but his memory will last forever in our hearts
Legends never die
Thanks for everything Maestro."
Blatter also used his Twitter account to give his own tribute: "Sad to learn of Di Stefano's passing, the most complete player I've seen
My favourite player
A legend is gone
RIP."
And Pele spoke of his sadness at the news, saying Di Stefano was responsible for breaking down barriers within the game
The Brazil great tweeted: "Back when we played, Santos and Real Madrid were for many years primary rivals, for having the best football teams in the world
"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."
Source : PA
Source: PA