Cassetti came off the bench to net a late winner for Roma.
"The derby is too important a game. Apart from the good football, what really counts in the end is winning," Totti said.
"Roma did it towards the end of 90 minutes that were very intense. I am very happy for us and for our fans.
"If I have to give a particular embrace to one of my team-mates then I cannot but give it to Cassetti who deserved this goal both as a player and as a man."