The Chelsea legend has moved to Pellegrini's Manchester City side on a loan deal until January, as his new side, New York City FC - who are part-funded by the Premier League champions - will not join Major League Soccer until 2015.
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However, when asked by reporters if he thought that the move had been conducted properly, Pellegrini responded: "I think so.
"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 dumbfounded by the reaction of some Chelsea supporters who were disappointed to see Lampard move to the Etihad Stadium after 13 trophy-laden years at Stamford Bridge.
"The problem was not that Frank Lampard did not want to sign another contract with Chelsea - Chelsea didn't want him anymore," he added.
"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."