Nigel de Jong's late goal saw Milan to the round of 16 win at San Siro after they had been pulled back just after the hour-mark.
Giampaolo Pazzini's neat 38th-minute finish put the hosts ahead but Nicola Sansone's penalty drew the visitors level before De Jong's volley four minutes from time.
Inzaghi lauded his players for their response to conceding the penalty.
"The penalty was a blow but the team did well after the penalty and showed character and reacted after 10 difficult days," he told a media conference.
"Against Torino it was a hard match but in the team's growth there will also be negative days. I never got ahead of myself and I won't get down now.
"We now have to recover our energy for Sunday."
Inzaghi's men have work to do in Serie A, sitting eighth after a three-match winless league run.
The 41-year-old is unfazed by the criticism being aimed at him.
"The criticisms don't affect me. It's disappointing to read fabrications but we will move forwards," Inzaghi said.
"I have always said that to remain at a certain level we must always give our all. We've had a tough week.
"We weren't Milan for various reasons, which we've analysed. Players are now coming back and I think as of tonight we already saw some important signs."
