Actors Phillip Jackson, Harry and James Armes, who star in Believe, and the former Manchester United manager's son Sandy Busby took part in the screening at the National Football Museum in Manchester last night.
The film, directed by David Scheinmann, is a fictional tale about the Bellshill-born legend coaching a team of young working class boys captained by a talented, but unruly player.
Busby tracks 11-year-old Georgie Gallacher down after an act of petty crime but, upon discovering his footballing talent, decides to come out of retirement for one last coaching challenge - to transform a young group of scallywags into a dream team to compete for the Manchester Junior Football League Cup.
Sir Matt, who died in 1994, played for Manchester City and Liverpool before taking over as manager of Manchester United, a position he held between 1945 and 1969. He pioneered a youth training system and famously created the Busby Babes, the youngest team in the country. He led United to victory in the 1968 European Cup Final.
Cox has said he is fascinated by the fact Busby came from a mining village in Scotland, like other managerial greats Jock Stein and Bill Shankly.
In 1958, Sir Matt was injured and half of his team were killed in the Munich air disaster. The film references the impact the tragedy had on Sir Matt.
Speaking about Sir Matt's experience in the crash, Cox said: "I think it was such a major, major blow in his life, losing all those extraordinary young men. I think he carried that with him. He had to start again. "