Inter striker Lautaro Martinez scored twice as they fought back to beat Fiorentina 2-1 and secure a second consecutive Coppa Italia title at the Stadio Olimpico.
"It’s disappointing, but we have another final to prepare for and two Serie A games, so we cannot let go now; we must remain concentrated," Italiano told Mediaset.
"We will try to avoid making the same mistakes that we saw tonight because that too will be a one-off match against a quality team, but if we play with the same spirit seen tonight, I think we can again cause problems for our opponents."
Fiorentina became the first club to reach the finals of four different UEFA competitions with their victory over Basel last week in the Conference League semis. The Italians made their first European final in 33 years.
Italiano remains confident that their Coppa Italia final defeat will not have a negative impact on the team's morale.
"We are accustomed to ... getting right back on track," he said. "I tell the players that when you fight with heart and sweat for the shirt, you never really lose."
Italiano said he was pleased with his side's spirit despite their defeat.
"I don’t think Fiorentina were embarrassed at all today, quite the opposite. I congratulated the lads, they deserve that for their spirit and determination," he said.
"We all would’ve given who knows what to lift this trophy and we didn’t manage it."
Fiorentina face West Ham in the Conference League final on June 7 in Prague.
