Italian boss admits that the club were after the duo but were unable to splash the cash as they had to adhere to Uefa's financial fair play rules limiting expenditure
The Real Madrid man eventually joined De Rossi at Roma by agreeing to a season-long loan.
"Gago is a player who we liked a lot. In the end we couldn't spend any more money due to the financial fair play rules," Mancini said, according to The Sun.
"But De Rossi is one of the best midfielders in the world. I have always thought that.
"But he is Roman and a Roma fan so I don't believe he will ever leave them."
City eventually signed former Manchester United midfielder Owen Hargreaves on a free transfer, and coach David Platt believes that his signing is a calculated risk.
"For a few weeks we have understood, from a business perspective, that after signing Samir Nasri, there wasn't going to be a big name coming in," Platt said.
"You have to get creative. The owners and the board have been terrific in saying, 'We know you need a midfield player but we have to be creative about it'.
"I think gamble is too strong a word. When you put all the things into the mix it's a calculated risk, and one we feel is well worth taking."