Hundreds of mourners attended his funeral service in Glasgow, including Ferguson and famous Celtic faces such as current manager Neil Lennon and a number of current and former players.
Ferguson addressed the congregation at the Church of Christ the King, Glasgow, to pay tribute to "a great man''.
He said: "I think it's very difficult for people who are successful to remain humble, it's a touch of greatness. Sean always had that greatness.
''Through his background, his upbringing, his Irishness, that breeds humility and also loyalty, he would never let you down.''
Although Ferguson was a supporter of rival Glasgow side Rangers, he formed a strong friendship with Fallon as he built his career as a coach and a manager.
He praised him for his role as assistant manager to Stein and said he was talented in the position, which required him to "get to the heart of the dressing room, make sure you know what's going on and you can help the way the manager sometimes cannot help''.
Ferguson also spoke of Fallon's skill in developing young talent and working with Stein to create arguably the greatest Celtic team of all time.
He said: ''That was the structure that I think helped Celtic become great and to become the first club in Britain the lift the European Cup.''
The Old Trafford manager also shared some personal insight into how well the pair knew each other.
He said: ''Over these years he became a great friend of mine and a great supporter of me. He had great observation, which I must say only (his wife) Cathy's got.
"He said he could tell, watching me on the telly, when I'm angry and when I'm happy. I thought I was always angry.
"What a fantastic man and it's a privilege for me to be here.''
Among the mourners were other Celtic veterans including Kenny Dalglish and Tommy Gemmell, who scored against Inter Milan when they won the European Cup in 1967.