"I think the humility, the fact that we are a united group, showing our qualities, that's what made this important result and we brought it home," said Greggi, who came off the bench in the 77th minute of Wednesday's encounter.
The raucous Italian crowd urged their players on, with chants of "forza Italia," and the Stade de Geneve lit up when Cristiana Girelli found the net twice in the second half, including a 90th-minute winner.
"There were a lot of emotions in that (second) goal. It was the whole journey we took, the sacrifices we made, and in the end, we reached the semi-final," Greggi stated.
"It was a fantastic feeling. We almost didn't believe it at the end of the game," said Michela Cambiaghi, who also came on in the 77th minute.
Italy defender Elena Linari said the 35-year-old Girelli was an inspiration for the team.
"Now we're going to put Girelli in a display case to rest for the semi-final - she deserves it all, and she's such a huge inspiration for us," Linari said.
It was the first time since 1997 that Italy had reached the semi-finals at a European Championship.
"It was achieved with effort and many sacrifices - today we have shown that we can do very well," Greggi said.
Before the match, Italy's coach asked his team to close their eyes and think back to the first time they had touched a football, Barbara Bonansea said.
"The feeling I have now is exactly the same. The stadium was packed, the energy was incredible. This achievement fills my heart," she added.
