Pellegrini was reacting to comments made by Arsene Wenger about the deals, questioning whether City had breached Financial Fair Play rules in signing Lampard on loan from New York City FC, their sister team in America.
City were hit with sanctions from UEFA for breaching regulations in May, and when asked about the Lampard deal, Wenger said: "Is it a way to get around the fair play? I don't know."
And Wenger also commented that he felt City had been courting former Arsenal full-back Sagna for some time, claiming the move was "agreed a long time ago".
The subject was predictably broached at Pellegrini's press conference ahead of the Community Shield clash with Wenger's side at Wembley on Sunday, and when asked if the deals had been done correctly, he said: "I think so."
He also admitted his surprise at Wenger's quotes, adding: "I think as managers we have enough problems with our own teams to be talking about other teams.
"The only thing I can say is that we have important restrictions about the amount of money we can spend, and Frank Lampard was a free player - we didn't spend any money in bringing him from New York City to Manchester City."
Pellegrini was also mystified at the reaction of some Chelsea fans over Lampard's move north after 13 years at Stamford Bridge.
He said: "I don't understand the reaction of Chelsea fans who say he is a traitor.
"The problem was not that Frank Lampard did not want to sign another contract with Chelsea - Chelsea didn't want him anymore.
"He is a competitive player, he will be important for our team and we didn't spend any money on him, so the rules of financial fair play don't have any relation with Lampard."