Calzona took over from Walter Mazzarri for the final months of the season at Napoli in a caretaker capacity.
However, after an initial boost, Napoli continued to struggle under the Slovakia coach.
He told La Repubblica: "I really wanted to do well on the Azzurri bench, I'm very attached to the city and the team: for this reason I'm still sorry that the results weren't what we hoped for, beyond the improvements highlighted by quite a few parameters. In football it happens.
"They put the label 'assistant' on me, but I've always been a coach. Does the assistant surgeon know how to operate or not?
"I love Napoli very much and I wanted to help the team. But the season had taken a bad turn and there was no way to reverse the trend. I will never regret having accepted the double role, I hold on to the pride of having coached Napoli, even if it lasted for three months and it didn't go as I had hoped.
"I hope the Azzurri return to the top and I look forward with my head held high, without bitterness. I am on a mission for Slovakia and I am very proud of it."