The Nottingham-born manager recently celebrated his two-year anniversary in charge of the Silkmen and his death has left the Cheshire club deeply shocked.
Rance said: "We're all absolutely devastated.
"I spoke to Keith last night at about 11.15pm after our game at Notts County and he was in good spirits because, although we lost, we had given a team chasing promotion a good game.
"We were chatting about an FA hearing after he had a row with a referee at Bournemouth, which just shows how passionate he was about the game.
"It was perhaps fitting that the last conversation we had was about football."
The exact cause of Alexander's death remains unclear, but Rance said: "He went home after the game last night and collapsed. Tragically, he never recovered."
Alexander had built a reputation in the lower leagues for working effectively within a tight budget and had previous managerial spells with Lincoln and Peterborough as well as a director of football role at Bury.
Along with MK Dons boss Paul Ince, Alexander was one of only two black managers working in English management throughout the 92 clubs.
Rance added: "Keith was the perfect manager for a club like ours.
"He was totally pragmatic about managing in League Two and the constraints involved.
"He was a splendid man, a real gentleman and an absolute privilege to work with.
"He was strong, sensible, commanded respect throughout the game and was unique in many ways."
Macclesfield are scheduled to play Hereford at Edgar Street on Saturday but the match could be postponed.
Rance has already spoken to Hereford chairman Graham Turner and explained: "Graham also knew Keith very well and the decision as to whether Saturday's game goes ahead will be taken by Keith's family shortly.
"I know what Keith would have wanted, but it will be his family's decision."
Alexander spent a successful spell in charge at Lincoln between 2002-06, helping the club to the play-offs for four consecutive seasons - the only manager to achieve that feat.
Imps chairman Steff Wright said: "Over and above being the absolute professional in everything he did, Keith was one of the nicest guys you could ever wish to meet.
"It goes without saying that our thoughts are with Helen and the family at this extremely difficult time."
The most notable spells of his playing career were at Grimsby and Stockport, while he also had a stint with Lincoln, where he later become manager.
He took charge of the Imps for the first time in August 1993, becoming one of the first black professional football managers in the UK.
His stay lasted less than a year but, after spells with Ilkeston and Northwich, Alexander returned to Lincoln as director of football and assistant manager before eventually replacing Alan Buckley at the helm.
It did not take him long to become a fans' favourite at Sincil Bank.
In November 2003 Alexander suffered a cerebral aneurysm and he was taken to hospital for vital surgery before returning to work in February 2004.
He left Lincoln by mutual consent shortly after the defeat to Grimsby in the 2005/2006 season, and then had a spell in charge of Peterborough before taking the position of director of football at Bury.
He took charge of Macclesfield in February 2008, but his health recently took a turn for the worse when he was forced to miss the goalless draw with Accrington last month due to illness.
Alexander had a spell at Bury in the 2007/08 campaign working as the club's director of football.
A Shakers spokesman said: "Keith Alexander was one of the most genuine people you could work with, to know and to have the pleasure to meet.
"There are a lot of heavy hearts around Gigg Lane this afternoon and as a club, we wish to pass our condolences to Keith's immediate family, his friends and all supporters, players and officials at Macclesfield Town Football Club."
Macclesfield assistant manager Gary Simpson has added to the tributes to Alexander.
Simpson told Sky Sports News: "He was a larger than life character - an honest man, a splendid man and will be missed by not only football people but people in all walks of life. He was an absolutely superb human being."
He added: "He was always there and together we just got on with stuff. In the difficult times we've had, we've helped each other through things and he was just a rock."
Football League chairman Lord Mawhinney has also given his reaction to the sad news.
He said: "I am shocked and deeply saddened by the death of Keith Alexander.
"The thoughts of the Football League, its clubs and football supporters everywhere will be with Keith's family and friends.
"He was a tough, dogged competitor as a player and as a manager and will be greatly missed."