A 99th minute extra-time winner from Davide Frattesi saw Inter triumph 4-3 on the night and reach the final 7-6 on aggregate.
Paolillo told L'Interista: "I feared a heart attack first for Frattesi, then for me because we all risked it. A wonderful match, no one can say that Inter didn't fully deserve this historic achievement. Everyone, from the first to the last player.
"It was like Italy-Germany 4-3: it's already in the history of football.
"It would be crazy to say that I expected it, it shows the greatness of this team. Character, technique: fantastic."
Inter can beat both Arsenal and PSG
Asked about the preferred opponent for the final, he continued: "I would prefer PSG, but I am convinced that both are beatable. They are both great, but I am convinced that this Inter can think of beating anyone.
"(Simone) Inzaghi has given a great game to this team, it's beautiful to watch and it's a huge group. The credit goes to him.
"The group, the skill of Inzaghi in creating it, of (Beppe) Marotta who chose Inzaghi and built this squad. You can see it when they celebrate how united they are."