He was renowned for his eye for talent and many of the greats he signed for the Glasgow club were there to pay their respects, including Kenny Dalglish, Pat Bonner and David Hay.
The Requiem Mass was held in his long-time parish at Christ the King Church in King's Park.
The former player and assistant manager died with his family, peacefully, at the age of 90 last Friday.
Celtic boss Neil Lennon was also present with many of his players, including Scott Brown and Georgios Samaras, as was Rangers manager Ally McCoist.
Mr Fallon's wife of 54 years Myra was accompanied by daughters Marie Therese, Louise Ann, Collette, Siobhan and Sinead and son Sean. He had 19 grand- children with another on the way.
Sisters Marie and June were also present.
Lisbon Lions present included Billy McNeill, Bertie Auld, Stevie Chalmers, Jim Craig, Tommy Gemmell, Bobby Lennox, John Clark and John Hughes,.
Welcoming mourners and honouring his allegiance to Celtic Father Desmond Keegan said: "Like the huddle so many people look to put their arms around the Fallon family."
The priest recounted how he has first met Mr Fallon when he was at primary school with his daughters. The footballer organised a trip to Parkhead for the school and spoke with "pride and passion" about the club.
He described him as a "humble" man who was so proud of his family.
Father Keegan talked of the times he played golf with the former footballer, who "got better and better" at the sport under pressure.
"Sean was no angel but he was an angel with a dirty face at times," he said.
The priest then invited "papa's" grandchildren to lead the bidding prayers.
One simply said: "I love you."
The Lake Isle of Innisfree was played during the service.
Manchester United boss Sir Alex Ferguson paid tribute to his long-standing friend.
Sir Alex spoke fondly of his friend who he learned from as a player and manager.
He said: "What he did for Celtic in bringing through all those players was fantastic."
Son Sean also paid an emotional tribute to his father during the service. He spoke of a "humble and generous" father.
"Dad never turned down a charity request," he said.
He told how Lou Macari gifted him his football boots from the 1978 World Cup because, "your father was so kind to me."
He said the legacy of Celtic's European Cup win would remain with the Fallon family for generations.
The service was followed by a private burial at Philipshill Cemetery in East Kilbride.
A reception for family and friends was held at Celtic Park.
A Mass to mark his passing was also being said today in his home town of Sligo, Ireland.