Totti, 34, was believed by many to be the undoing of Ranieri at Roma.
After a highly successful first season in which Ranieri turned around a team that lost its opening two league games to come within a whisker of stealing the Serie A title from Inter Milan, his second campaign ended in resignation.
Roma struggled all season to repeat the feats of the previous campaign and Ranieri walked before he could be pushed in February following a 4-3 defeat at Genoa after having led 3-0.
A feature of his tenure was his willingness to leave Totti on the bench last season with Marco Borriello his preferred centre forward.
That was a move that often riled fans and the Rome-based pro-Roma press, particularly when things went badly.
Totti is held in such high esteem amongst Roma fans that a common joke is that he is second only to the Pope in the city.
But former Chelsea, Juventus and Atletico Madrid boss Ranieri admitted he was unimpressed with his dedication to training.
"Sometimes Totti didn't train as he should have done from Monday to Saturday and so (on Sunday) I put him on the bench," said Ranieri.
"But he's the best player I've ever trained.
"If he'd left Roma for Barcelona or Manchester (United) he would have won the Golden Ball several times.
"I trained (Frank) Lampard and (Alessandro) Del Piero; the first was dedicated to the point of sacrifice while the second never went home (from training) and called his team-mates back to play, to practise shooting, take free-kicks and penalties, he made demands on the goalkeepers.
"Totti, however, went straight home. Football-wise Francesco was better but Lampard and Alex have strong characters."
Ranieri hits out at "lazy" Totti
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