The midfielder marked his Lazio debut with the winning goal in Monday's 1-0 victory at Bologna, coming off the bench to convert Boulaye Dia's flicked pass just after the hour mark.
Speaking afterwards, Frattesi reflected candidly on the toll his last season at Inter had taken on him personally, even as he stressed his fondness for the club he left behind.
"My last year with Inter had brought me to a bad place personally, and it hurts to say that because I was really happy there and I'm still in touch with everyone. But I felt that changing scenery to find new motivation was the right choice. For a player, that's fundamental," Frattesi said.
He added that a change of environment tends to bring out the best in him: "When there's a desire for a new adventure, you give your best. I knew it would go well, even if I didn't imagine it would go this well — I couldn't have asked for more."
The victory carried particular significance coming just days after Lazio's Coppa Italia exit to Mantova, a result that had cast an early shadow over Gennaro Gattuso's start in charge.
"This win means a lot — during the week we'll be able to work calmly without a lot of unnecessary fuss, and it's also good for the mood and for the group," Frattesi said. "I've found a really good group here, a very important one. It had been a while since I'd been part of a group without hot heads or strange characters — I'm genuinely happy to be working with a group like this."
Frattesi also walked through the winning goal itself, crediting his positional awareness for the finish.
"The dedication for the goal is the usual one, to my girlfriend and my family — hopefully there will be plenty more to dedicate in the future. As for the goal, I looked behind me, saw Dia, and tried to get the ball to him before making my run into the box. Sometimes that ball doesn't arrive nine times out of ten, but when it does, you put it away."
The result gave Gattuso his first win since taking charge of Lazio, following the disappointment of last week's Coppa Italia elimination, and offered an early sign that his summer signing could prove a significant asset off the bench as the season develops.