Ranieri was dismissed by Leicester in February, just nine months after guiding the club to a remarkable Premier League title.
And Prandelli, who resigned from his post as Valencia boss after just 10 games in December 2016, confirmed that he was approached by the English champions.
"New coaches should study his situation. In two or three months, what happened cannot happen," Prandelli told SFR Sport.
"Subconsciously, the team clearly gave less and worked less than it could've done. That is why it's important for a club and directors to not leave all the responsibility on the shoulders of the coach, otherwise this happens.
"There was an approach [from Leicester], but I immediately said no. You don't go to a place like that after seeing how Ranieri was treated. You don't go there. Full stop.
"Football management is an extraordinarily difficult, but wonderful job. In recent years there are big changes between the way coaches and players deal with each other.
"For example, Ranieri achieved something extraordinary that could not be repeated. A coach who wins a memorable, historic title and is then dumped after a few months.
"When responsibility is all on the shoulders of one person, he can't hold it. If that responsibility is shared with the club, directors and players, then it becomes far simpler.
“A coach needs to just be a coach. When he is asked to do other jobs, it becomes complicated."
Since Ranieri's dismissal, Leicester have won all four outings under caretaker boss Craig Shakespeare - progressing into the quarter-finals of the Champions League while moving six points clear of the Premier League relegation zone.