Reflecting on his decision, Allegri – who arrived from AC Milan in 2014 – told magazine Stile Mese: "I said 'no' to Real Madrid because I made a commitment with the president."
Allegri did concede Madrid the title of the world's "biggest club" but believes it was the correct call to remain.
"Therefore, my maximum respect for Juventus and given word were why I rejected the call of Real Madrid, the biggest club in the world and the dream for every coach.
"I'd be a hypocrite if I said I wasn't honoured by their consideration, but I'm absolutely convinced that I made the right decision."
Allegri also dismissed being placed in the pantheon with some other Juventus legends, including recently-departed goalkeeper Gianluigi Buffon, because he has not been with the club long enough to reach that level.
"Am I a 'bandiera' like Buffon or Del Piero? I absolutely don't want to be equated with them because they're players who wrote Juventus' history, whereas I've only been here for four years."
Seeking an eighth consecutive Scudetto, Juve open their Serie A title defence against Chievo on August 18.