Vieri spent six seasons with the Italian giants between 1999 and 2005, in an otherwise nomadic playing career, whilst Moratti was president of the club from 1995-2013.
The former Italy international had his contract terminated after battling with injury problems and he admits he is sad at the way his time with the club came to an end.
"It's really a shame that it ended in a certain way," the 41-year-old told Gazzetta dello Sport.
"I loved Inter, I gave everything [to the club]. I would have killed for the Nerazzurri shirt, every day.
"At training I was the first to arrive and the last to leave. I never pulled back.
"My relationship with Moratti was special, strong, very strong.
"We spoke several times during the day, even at three in the morning, we talked about everything. It made me feel part of the family.
"So you understand the terrible disappointment when I found out that I was shadowed and even intercepted. Heck, these are things you do with the mafia.
"But I know how things are going, especially in football. It was enough to speak to me directly, and I would not have had a problem leaving on good terms."
Despite his disappointment at the way he left the Nerazzurri, Vieri is adamant he harbours no long-term grudge concerning the club where he enjoyed his best spell of his career.
"I could never hate Inter, this is clear to everyone," said the retired striker.
"It's impossible, they were my best years. I suffered, rejoiced and felt emotions that I have never experienced anywhere else.
"Those emotions were unique because we lived through it with the fans. We were the strongest, and that attendance was around us.
"I remember arriving at the stadium an hour and a half before Inter-Verona, but inside there were already 85,000 people screaming your name. Stuff like this gives you chills, it's impossible to explain."