The Italian, who was sacked days after losing in the FA Cup final to Wigan back in May, said:
I'm happy that Manchester City is one of the best teams in England because I built this team.
The players that score the goals are players that I bought - Sergio Aguero, Edin Dzeko, Yaya Toure, David Silva and Samir Nasri.
When you work, you know you can have some problem with the players, this is normal because the manager wants the players to work hard, play well and the players should understand this.
When you change the manager, it is better maybe, because you change the way to work.
I think Pellegrini is doing a good job but what is happening now at Manchester City, we did three years ago. It's the same.
After four or five years, maybe the manager needs to change team. I did my job, I built a fantastic team, we played fantastic football and we didn't win last year only because Manchester United bought Robin van Persie.
He was the difference, if not I think that would have changed the history in Manchester over the last three years. We played really good football and now they are continuing to do this.
Mancini, of course, deserves great credit for the work he did during his time in charge. He took over for Mark Hughes, a man who had spent big and delivered little during his 18 months at the helm, leaving behind a side shambolic defensively, which had won just two league games in 11 matches.
As this BBC Sport article details, Hughes spent close to £200 million during his brief stint, yet his side finished 10th in his only full season in charge, one place lower than under previous manager Sven-Goran Eriksson, who had far more financial restrictions placed on him.
Players such as Joleon Lescott and Micah Richards, who would later go on to be vital parts of City's title-winning campaign under Mancini, struggled badly under Hughes, despite his insistence that his backroom staff were "the most qualified in the Premier League".
He saddled the club with a string of under-achieving high-earners and failed to get a good run of form going at any stage. It was undoubtedly one of the poorest managerial performances of recent times.
Mancini changed all of that. City were instantly much more difficult to beat, and although he couldn't deliver Champions League football during his first six months in charge, he went on to win the FA Cup in 2011 and, in the most dramatic circumstances imaginable, the league title in 2012.
He had managed to change the whole culture and mentality of the club. City's first major trophy in 35 years and first league title in 44 years, delivered by a man who had fallen in love with the club and whose fans had fallen in love with him.
His City team were pragmatic and defensively sound, but also capable of brilliance. By adding David Silva, Sergio Aguero, Yaya Toure and Mario Balotelli, Mancini brought flair and beauty to City's attack.
But the flair and beauty eventually disappeared.
The players who once fought with everything they had suddenly seemed to dislike Mancini's methods. His grip on the dressing room slipped badly, and City once again exited the Champions League at the group stage, before giving up their title with a whimper—a limp submission that allowed Manchester United to waltz unchallenged and reclaim the trophy City had worked so hard to secure.
The FA Cup final defeat to Wigan, a side on their way to the Championship, was the last straw for City's board.
It didn't help that he consistently broke ranks and openly criticised club officials, with Brian Marwood often the target of his ire. City's owners prefer to keep issues in-house, and Mancini wasn't playing to their tune.
His aggressive, autocratic leadership style eventually rubbed people the wrong way, and, sadly for City, that disharmony was all too clear on the pitch during his final term in charge.
This season could hardly be more different. Under Pellegrini, City are playing better football than at any time under Mancini, with ruthless efficiency and an insatiable appetite for goals the hallmarks of their season.
Pellegrini has added Alvaro Negredo, Fernandinho and Jesus Navas—and revolutionised the squad. They are on an 18-match unbeaten run—four short of the club's 67-year-old record—and have scored 106 goals, more than they managed throughout the whole of last season.
The difference is clear: City are producing football above and beyond what they've managed before, are into the Champions League last 16 for the first time and have secured a trip to Wembley for their first League Cup final appearance since 1976. This is a step up for the club.
Mancini will forever be remembered fondly by City's fans, but his deluded comments to the BBC, which are probably borne out of a deep desire to still be manager of the club, should not detract from the job Pellegrini is doing.
Rob Pollard is Bleacher Report's lead Manchester City correspondent and will be following the club from a Manchester base throughout the 2013-14 season. Follow him on Twitter here @TypicalCity.