Despite going behind early on - just as they did in the first leg - the Giallorosse roared back to win 4-1 at Stadio Tre Fontane, and confirm a 6-2 aggregate victory in the tie.
Spugna's side will find out their group stage opponents on Monday.
Here is what the coach had to say after the game...
How big of an achievement is this for the club?
"It's a massive achievement. We are pleased, we've put in two great performances. Today we started with a slight advantage - but that was wiped out after 20 minutes.
"But we did a good job of taking back control of the game, taking things into our own hands and creating lots of chances and scoring as many goals as we did. It was a great occasion in front of a great set of fans."
A third straight comeback win for the team - how is your heart doing?
"Right now, not too bad. But I hope that we don't have to keep producing comebacks. But it nevertheless shows that the team is in a good place mentally and physically, because it's never easy to overturn a scoreline."
What is waiting for Roma in the group stage of this competition?
"Whatever it is, we are ready to go and face it. Being there means we are among the 16 best sides in Europe, and that's an amazing thing.
"We need to push forward with courage and conviction. We want to test ourselves against the very best on the continent. Let's see what the draw gives us, but we are certainly going to be up against some top sides.
"But, right now, we are just curious to find out. I think that we will be able to enjoy ourselves, though, and perhaps upset a few sides along the way."
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