The Gunners boss recently commented that City's loan signing of Frank Lampard could be a sign of things to come, in regards to the club using methods to sign players without spending money on transfer fees.
Lampard will join New York City FC, owned by Manchester City, for the next MLS season and has linked up with Pellegrini's side on a short-term loan.
Wenger appeared unhappy with the deal as it has allowed City to make a big signing within the rules of FFP - but in a manner that is unfair on those sides that don't own other clubs.
However, Pelllegrini was dismissive of the Arsenal manager's claims and insists Manchester City have done nothing wrong in bringing the former Chelsea midfielder to the Etihad Stadium.
"I think that as a manager we have enough problems worrying about ourselves without talking about other teams," he told reporters ahead of his side's Community Shield clash with the Gunners.
"What I will say is that we have important restrictions over FFP. Frank Lampard was a free player so we didn't spend anything to bring him here from New York City."
City face Arsenal at Wembley on Sunday, making the timing of Wenger's previous comments all the more intriguing.
Initially, the Frenchman said: "It looks like all of these 'City' clubs will feed the main club Man City. I heard they want to buy five clubs across the world.
"At the moment the players they sign cannot play until next year so they will register them in the clubs and they get out on loan.
"Is it a way to get around the fair-play? I don't know. We are happy to dedicate the money to just run our club – there is not a lot of surplus to run other clubs."