Trailing 2-0 on the night - and the same score on aggregate - Inter staged a stunning fight-back to win the second-leg 3-2 at San Siro stadium.
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Thuram said afterwards: "It was a fantastic match, winning two trophies would be wonderful after the season we've had, also for our fans."
Teammate Petar Sucic also stated: "Of course, I'm very happy; it was fantastic, and in the end, I think we deserved this victory. It's never easy against them; we also came back against them in the league.
"We demonstrated our mentality once again. I wanted to win when I came here, and doing so in my first year would be fantastic.
"Let's hope we win both the league and the Coppa Italia."