Totti's second-half strike was enough to give Aurelio Andreazzoli's side the victory against the Serie A champions and the 36-year-old believes that the win showed how the strong the team is.
"Only with great character could we beat a team like Juventus," he told reporters after the game.
"It was normal that at the start we were timid as we are coming off a difficult time [following Zdenek Zeman's recent sacking], and Juve are among the best teams in Europe.
"I hoped for this, as we don't deserve our current position. The team always try to give their all for ourselves and the fans."
The win moved Roma up to seventh in Serie A, with Juve staying top.