The 34-year-old spent three years at the club but was informed that his services were no longer required, resulting in a move to Serie A rivals Juventus.
“I think that was an act of ingratitude from the club, given the way that things developed.” The Brazilian told UOL Esporte.
“They could have told me the truth sooner. Instead they waited until the end of the season to tell Julio Cesar and myself to find a new club.
“Inter showed a lack of consideration towards us.”
The experienced defender signed a two-year deal at Serie A titleholders, Juventus and insists he is happy to have embarked upon a new chapter.
“The fans now tell me I am at a real club, that I need to forget Inter," he added.
“In the future, I want to return to Brazil. But for now, I want to play two more years in Italy.”
Lucio made 96 appearances for the Nerazzurri, scoring three goals and winning the Champions League with them in 2010.