The Italian locked horns with the Scot since taking charge at the Eithad Stadium, snatching the 2011-12 Premier League title away from Manchester United thanks to a last-gasp Sergio Aguero goal on the final day of last season.
Mancini described Sir Alex as the best manager of his generation and is unsure whether his achievements in the English game will ever be eclipsed.
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"It was a great honour to beat him in Old Trafford and I wish him good luck for his future. I don't know for which reasons [he has retired].
"For me it was fantastic to compete against him in every derby because he was a top manager. I think we should respect his decision.
"Everyone can have his opinion but one manager who stays for 27 years in the same club and won every trophy for 27 years - it is an incredible situation.
"I don't think there will be another manager like him. It is difficult to say Sir Alex is the best but he is the best in the last 27 years."
Yaya Toure told reporters on Thursday that he hoped Sir Alex's retirement would lead to a period of dominance for City, but Mancini believes the foundations left by the Scot will see their rivals prosper for some time.
He continued: "I think that when there is a top club like United, you can change the manager, an important manager like Sir Alex who built this team, but I think the club will stay a big club."It has a big history. I don't think that will change."