City went on to win the Second Division crown in 1966, the League title in 1968, FA Cup in 1969 and European Cup-Winners Cup and League Cup in 1970.
Allison managed 11 clubs at home and abroad, leading Sporting Lisbon to the Portuguese League and Cup in 1982.
He took charge of Crystal Palace on two separate occasions, and also had spells as manager of Bath, Plymouth, Galatasaray, Toronto City, Middlesbrough and Bristol Rovers.
During his playing days, Allison made more than 250 appearances at centre half for West Ham, before losing a lung as the result of tuberculosis in 1958.
"Big Mal" - as he was known - always had an eye for publicity, and was famed for the "Lucky Fedora" he wore during one of Crystal Palace's Cup runs and his love of cigars - but his later years were dogged by ill health.
Your tributes to Allison
A statement on the Manchester City website read: "Flamboyant, brilliant and larger than life, Malcolm will be sorely missed by everyone at the Club and beyond."
City plan to pay tribute to Malcolm at the forthcoming game against Arsenal, and have also pledged "an appropriate commemoration to his life and work in the memorial garden at the City of Manchester Stadium".
Mike Summerbee told BBC Radio Manchester that Allison was "the greatest coach this country ever had. And still is, without a shadow of a doubt".
MALCOLM ALLISON QUOTES
"A lot of hard work went into this defeat""You're not a real manager unless you've been sacked.""John Bond has blackened my name with his insinuations about the private lives of football managers. Both my wives are upset.""A lot of people in football don't have much time for the press; they say they're amateurs."
He added: "Joe Mercer was the figurehead but Malcom Allison was the key to the door, really. He brought fitness levels to football that are still there now. He was the forerunner of fitness and tactics way beyond his time.
"We were doing things in 1965 on running machines at Salford University with massage based fitness, we trained in Wythenshawe Park with Derek Ibbotson and some of the Salford rugby league lads - that's how hard it was and how good it was.
"He was just quite an amazing man. A great personality and a well read man as well, a very intelligent person. He was a character.
"His life was full, every day he lived his life and his enjoyment was a pleasure for us as well. We worked hard together and we enjoyed ourselves together and he was a great personality and gave you the confidence to believe in yourself as a footballer.
"It was the same when Joe Mercer died - when you lose someone of the calibre of Malcolm Allison as a coach, then it's very difficult to take, even though he's been ill for quite a time.
"My wife always says that 'you love Malcolm Allison more than you love me.' That's how you epitomised Malcolm Allison."
City life president and former general secretary Bernard Halford, who knew Malcolm for over 40 years, told the club's website: "We will never see the likes of him ever again, and he did so much for the club.
"The signing of [captain] Tony Book was a masterstroke, but he enhanced the careers of so many other players and they worshipped him.
"You knew he was in a room with you, not many people have that kind of presence but Malcolm did, and he transferred the confidence he had in himself to the team. He felt we could beat anybody and he wanted the players to think that way, too."
Source: BBC Sport