Inter Milan striker Esposito scored twice, including a penalty, while Frattesi added the goal that put Italy ahead in the second half after Michael Olise had given France an early lead.
“Winning against such a strong France team is a source of pride for all of us,” Esposito told Sky Sport after the match.
The 20-year-old also revealed the pressure he felt when stepping forward to take Italy's second penalty. His older brother Sebastiano had missed from the spot earlier in the second half, and Pio was determined to put that disappointment behind them.
“I had an extra responsibility when I went to take the penalty. As well as having to finish the game by making it 3-1, I also had to make people forget my brother Sebastiano's mistake,” he said.
“I won't deny that it weighed heavily on me when I saw him miss his penalty.”
The two brothers were both involved in the incident, with Roberto Mancini confirming afterwards that Pio was his first-choice penalty taker and Sebastiano was second.
Esposito has attracted considerable attention following his performances for club and country, but insisted that his approach has not changed.
“I have always done my job and given everything. The only secret is working every day,” he said.
He also credited the atmosphere within the national team, describing a group that combines emerging talent with experienced players.
“We have all started again together with great enthusiasm. Ours is a very young group, but there are also experienced players who help us. We have a really united group.”
Frattesi shared that assessment, believing Italy's ability to pull together after difficult moments has been central to their improvement.
“ I think it accounts for 60 or 70 per cent,” the midfielder told Rai. “The situations are similar. At Lazio, after the first defeat, we became more united, and I think that is the most important thing we have rediscovered with the national team.
“When there is enthusiasm and a willingness to suffer together, everything becomes easier.”
Frattesi also reflected on the significance of scoring at San Siro.
“Perhaps my brace against Ukraine served another purpose, but scoring here is always special. It was a really great day.”
The midfielder added that Mancini has encouraged him to develop different aspects of his game rather than become defined by one particular role.
“I have some discussions with Mancini. He wants me to improve the things I do less well, but also to make the most of my strengths, while I just want to improve what I don't have,” he said.
“I am happy to have the confidence of both Mancini and Gattuso.”
For both players, the victory was about more than their individual contributions. Italy's response to going behind, and their ability to recover after Sebastiano Esposito's missed penalty, provided further evidence of the togetherness they believe is developing within the squad.