Frattesi's 75th-minute equaliser, a first-time finish from a Mattia Zaccagni cross, set up Albert Gudmundsson's dramatic 88th-minute winner as Lazio came from behind to beat Udinese 2-1, extending their unbeaten start to three wins from three matches. It was the midfielder's third goal in as many Serie A appearances since arriving on loan from Inter Milan over the summer.
"It means a lot because it gives us even more enthusiasm after an unexpected start. I'd have signed for six or seven points, but the strength of this team is the group," Frattesi told Sky Sport after the match.
The result puts Lazio level with Roma and Inter at the top of the table, level on points after three rounds, though the midfielder was quick to play down talk of a title challenge this early in the season.
"It's early, too early. This is a very difficult league and we have other big tests ahead of us. It will be almost impossible to stay up there, but for as long as we're there we have to believe in it," he said.
Asked whether he had expected such a strong start to life at his new club, Frattesi admitted the form had taken even him by surprise.
"Honestly, no, but I've started to feel electric again, and for me that's a great thing that I'd been missing," he said, a reference to the diminished role he had fallen into during his final season at Inter before his move to Rome.
Frattesi's goal continued a habit of decisive contributions since his arrival, having also scored the only goal in wins over Genoa and Bologna in Lazio's opening two matches.
His willingness to arrive late into the penalty area has given Gennaro Gattuso's side an attacking threat from midfield that was often missing during a ninth-placed finish last season, and his impact has been reinforced by the emergence of fellow new arrival Gudmundsson, who marked his own debut with the winning goal, a header from a Danilho Doekhi cross two minutes from time.