Frattesi's early finish, though not the cleanest of strikes, proved enough at the Olimpico as Lazio held firm despite late Genoa pressure.
De Rossi, whose side also lost their opener against Napoli without scoring, admitted his team had regressed.
"We took a step back compared to the Napoli game, today we were flatter. We built play but never gave the sense we were troubling Lazio. In the second half the reaction was more about nerves, and we only created chances in the final 20 minutes," he said.
"I have to work out how to fix what isn't working, but we have to say we've played Napoli and Lazio, two sides operating on a different level to us right now."
Asked what needed to change, De Rossi pointed to a lack of end product in the final third.
"We held the ball too much, and from the final third we're not going well - I have to work out how to get our players scoring goals. There are many ways to do it, we have to figure out which one," he said, before diagnosing a repeated issue from the opening two matches. "We made too many bad touches and lost the ball after winning it back. Even against Napoli we created a lot but had few shots on target - it's been the same 'illness', if I can call it that."
Gennaro Gattuso, by contrast, was frustrated only by a moment of complacency from his own side rather than the result. Asked about a heated exchange with full-back Pedraza, he did not hold back.
"There's little to say, the talking stops there - I don't like presumptuous people, you have to do the things we prepare. We could have read that situation better, we switched off, but it ends there," Gattuso said.
"We could have closed it out in the first half with Nuno's header. In the second half we were better on the counter, circulating the ball correctly - if I have to find a fault, it's that the ball moved too slowly in the first half. Tavares was excellent, creating three or four chances."
Gattuso reserved special praise for midfielder Reda Belahyane.
"He's training at a thousand miles an hour - in his first week he didn't finish a single session, but he put his head down and what you sow, you reap. Credit for these two wins goes to the lads, they believe in what we're doing," he said, before acknowledging a run of injuries. "We've lost three players in two matches, which is a shame, but with Belahyane, credit to him."
He added that Frattesi, six months without playing a full 90 minutes, had understandably tired late on after taking a knock to the knee, and dismissed any complaints over the officiating as not worth commenting on.