The Swede left the English Championship club by mutual consent on Monday after just one year in charge with Leicester lying 13th in the standings.
"I am disappointed to be leaving Leicester City Football Club," Eriksson said in a statement issued by the League Managers' Association on Tuesday.
"It was always my aim to lead the club into the Premier League and I am very sorry that I won't be able to do that.
"I have always thought, and still believe now, that the club will be promoted this season. The current squad is capable and ready to achieve promotion, but football is a results industry and unfortunately we couldn't quite get things right enough of the time."
Eriksson made his name in Italy where he won the Serie A title with Lazio and he managed England from 2001-06 before spells with Manchester City, Notts County and the national teams of Mexico and Ivory Coast.
"Being the manager of Leicester City was an absolute pleasure and I wish everyone connected with the club the best of luck," the 63-year-old said.
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