The Italian was fired on Thursday with Leicester one place and one point above the relegation zone.
"Yesterday my dream died," Ranieri said in a statement on Friday. "After the euphoria of last season and being crowned Premier League champions all I dreamt of was staying with Leicester; the club I love for always. Sadly this was not to be."
Ranieri's dismissal has been met with widespread shock.
"The adventure was amazing and will live with me forever," the 65-year-old manager said.
"My heartfelt thanks to everybody at the club, everybody who was part of what we achieved, but mostly to the supporters. You took me into your hearts from day one and loved me. I love you too."
Leicester started last season as 5,000-1 outsiders to win the English top-flight title for the first time in their history.
"No-one can ever take away what we achieved together and I hope you think about it and smile every day the way I always will," Ranieri said.
"It was a time of wonderfulness and happiness that I will never forget. It's been a pleasure and an honour to be a champion with all of you."
(Reporting by Ed Osmond,; Editing by Clare Fallon)
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