The victory has Roma just a point away from the leaders.
"On Saturday the passion, technique and aggression were poured out on to the pitch at the Olimpico," wrote Totti on his official website.
"These three elements allowed us to beat Inter, a great squad led by a great Coach and with a world class squad."
The 2-1 victory has put the Giallorossi within a point of leaders Inter and right back in the thick of the Scudetto race.
"I think any player would've loved to play in that big match. It was spectacular seeing all those people in the packed Olimpico, which didn't have a spare seat.
"It was moving to see and hear our fans singing for the entire 90 minutes. This is also a victory for the club, whose policy of keeping ticket prices low enables many of our supporters to stand by us in difficult economic times.
"I am certain that in the next few games we will see the same policy, which will allow our fans to crowd around by our side in this sprint finish."