Papu Gomez struck twice for the win in Rome.
“We created plenty of chances today and perhaps could've scored more after the break," Gasperini told Sky Sport Italia.
“This is a team that believes in itself and has reached a balance allowing it to face difficult games like this with a strong personality. I didn't need to remind them that last season we were 3-0 up here and drew 3-3, because this was a different game and the lads remained concentrated."
On Gomez, the coach continued: “It was an extraordinary goal. He is someone who can play absolutely anywhere and has reached his peak now. Papu works hard, but in the decisive moments of a match, he is able to give that extra spark of creativity that helps us bring results home.
“We're scoring a lot of well-worked team goals, and while you expect it of Papu, having Hans Hateboer score two games in a row is a sign of how much the team has grown.
“Our ambition is for everyone in the squad to have great feet and we'll never stop working on our technique. I think that is where we've improved the most over the last few years, because it's not true that all we do is run hard."