The 36-year-old became the second-highest goalscorer in Serie A history with the 225th strike of his career - matching the tally of former AC Milan forward Gunnar Nordahl.
Totti was greeted by his children after the goal, who presented him with a commemorative t-shirt.
"It was emotional and very unexpected because I didn't even know they were in the stadium because they've been sick all week," he told Sky Sport Italia.
"It was a very beautiful thing for me and it is an unforgettable moment."
Totti made his debut for the Giallorossi back in 1993.