Michael Olise gave France an early lead, but Francesco Pio Esposito equalised before Davide Frattesi put Italy ahead. Esposito then converted a penalty to complete his double and secure the victory.
Mancini was pleased with how quickly his players responded to his instructions, although he acknowledged there was still considerable work ahead.
“I have given what I can give. They have been good at taking it on board quite quickly, even though we know it will be a long road,” he said.
“After going behind, we could have conceded three or four goals. Instead, we did well.”
The Italy coach rejected the suggestion that the result was simply about courage, arguing that his younger players still needed to become more comfortable taking risks.
“We have to improve in this area. The young players need to try things that eventually become normal,” Mancini explained. “It will take a little time, and I hope the older players help them.”
He also defended his decision to use Sebastiano Esposito as the first penalty taker, with Pio next in the order.
“Because I am the coach, and I have to make decisions,” he said. “Pio was first and then Sebastiano. It was a family matter,” he joked.
Mancini was particularly enthusiastic about Pio's potential, suggesting the striker could become a prolific goalscorer for Italy.
“Let's hope he scores many more goals. Gigi Riva has been sitting there on 35 for a long time. Let's hope somebody surpasses him. We need Pio's goals and those of the others as well, but he can score a lot.”
Zidane, meanwhile, acknowledged that France had been unable to maintain their level after the interval.
“It's true that we started well and were good in possession, but in the second half we struggled, especially defensively,” he said.
The France coach rejected the suggestion that his players had lacked courage, insisting they remained competitive even as Italy took control.
“No, quite the opposite. We stayed in the game and did some good things in possession, particularly in the first half. In the second half we dropped off a little, especially after the 2-1 goal. It's part of the process.”
Zidane also refused to single out individual players, including Michael Olise, after France's performance declined.
“You cannot always play at a very high level for 90 minutes. Olise has played some good matches. He was not the only one who dropped off in the second half; it was the whole team.”
The defeat means France must beat Turkey in their final group fixture to guarantee their place in the Nations League quarter-finals. Zidane insisted that the team must focus on recovering before that match.
“We wanted to win tonight to avoid this situation on Sunday. We didn't manage it, so we will have to win the final match against Turkey,” he said.
He also accepted that France had not defended well enough, despite creating opportunities and enjoying periods of possession.
“The most important thing is creating chances. The woodwork played a part, but I am not disappointed because I would have been if we had not created good possession. What we need to analyse is that we were not at the right level without the ball.”
For Mancini, the result represented another step in rebuilding Italy's confidence. For Zidane, it provided a clear indication of the defensive work still required before the group stage concludes.