The Argentine midfielder is upset that he was only informed that he would not be offered a new contract a day before the final game of last season, against Chievo
The former Argentina international parted company with the Serie A side during the summer, bringing the curtain down on a 10-year stay at San Siro, but had thus far refused to publicly speak about the manner of his exit.
However, Cambiasso, who played a key role in Inter's treble triumph in 2010, has now revealed that, while he had no issue with the decision to let him go, he remains upset that he was only told that he would not be offered a new deal just before the end of the 2013-14 campaign.
"I'm not saying that I deserved to know three or four months beforehand but not the day before the final game, against Chievo," he told Sky Sport Italia.
"They could have even told me maybe a week before, given that I had spent 10 years at Inter."
When asked if he would have been treated with more respect by Erick Thohir's predecessor as Inter president, Massimo Moratti, Cambiasso replied: "Yes, probably, but the fact remains that I contributed to the realisation of [Moratti's Champions League] dreams.
The veteran turned down a move to Premier League outfit Leicester City earlier in Augyst but remains keen on a move to England. Indeed, the 34-year-old cannot see himself resuming his career in Serie A.
"I'm not capable of giving what I gave to Inter to another to another Italian team," he confessed. "This week I'll know better where I'm going; where I can be happy with my family. But wherever I go, I think that I'll sign a one-year contract. That's my choice."