The Italian, who was sacked on May 14 after a disappointing 2012-13 campaign, also revealed he would have gone all out to land "extraordinary" striker Edinson Cavani this summer.
Despite an agreement with Arsenal over Van Persie, the Dutchman eventually moved to rival Manchester United, while De Rossi remained at Roma and Hazard swapped Lille for Chelsea.
The signing of the Gunners striker helped propel United to the 2012-13 Premier League title and Mancini, who was axed by City back in May, rued the club's inability to land his top transfer targets.
"I wanted to change something after winning the title, I wanted to make three big signings so the team could be relaxed," he told Corriere dello Sport.
"I asked for Van Persie, we had an agreement, I knew he was ready to make the difference. And I also suggested to sign De Rossi and Hazard. But we didn't make any move."
Former Inter boss Mancini also revealed that he had Napoli striker Edinson Cavani lined up as a priority signing during the summer transfer window.
"If I had stayed at City, I would have done everything to sign Cavani," he added. "We were close to him. He's an extraordinary player. Also Fernandinho is my choice."
The Italian also praised his replacement, Manuel Pellegrini, and insists City struggled without Mario Balotelli following his January move to AC Milan.
"We missed Balotelli's goals, but he was unhappy in England. He, like [Luis] Suarez, was constantly attacked by opponents, referees, fans. It's also true that he didn't do anything to avoid some situations.
"Our fights? It was nothing. I just got angry with Mario after a rough tackle. Thirty seconds of verbal argument and it became a matter of discussion. Pellegrini is a good coach, it's logical he will do a good job. The team is top."