The 17-year-old was promoted to Lazio's Primavera side for the Scudetto playoffs and was expected to step up to the senior squad this season.
However, Marin missed training last week and, according to reports in Italy, went to Manchester to sign a professional contract with City.
Rules in Italy do not allow players under the age of 18 to sign professional contracts, and Lazio are furious that the Premier League champions have taken advantage of this without informing them.
"We don't know anything official yet, but it's clear the lad will no longer be playing with us," fumed Lazio's sporting director Igli Tare.
"He can go to City. Mancini acted dishonestly. He could've made a phone call and told us. That's no way to behave.
"In theory we could've signed Marin, but in practical terms we couldn't, because we would've had to do the same with another 10 teenagers in our academy. That would have wrecked the budget. The truth is that the current rules on young players in Italy have to be changed."
It has been reported in Italy that City manager Mancini and his assistant Attilio Lombardo held talks with Marin during the recent youth tournaments in Gubbio and Chianciano, convincing him to move to Manchester.