The 40-year-old, who retired in the summer after an unparalleled 25-year playing career with his boyhood club, was recognised for his remarkable achievements at a ceremony in Milan.
"'Legend' is a big word, but I am very happy to receive the first of these," Totti, who is now a director at the club, said.
"Would I still like to be pulling on my boots? Sometimes when I'm watching a game there are moments, but without me the guys are doing very well; with the coach, with the players.
"It has been the end of one career [this year], but also the start of another."
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Totti was asked if, after winning a title as a player, he hoped to soon win one as a director.
"I would gladly accept that outcome - I hope we can do it," Totti said, before praising new coach Eusebio Di Francesco.
"I knew his work as a coach, but I didn't think he was this good and also had such room for improvement," he noted.
"He is prepared, focused, assured: he is on the right path to becoming a great coach."
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