It sets up a meeting with SC Freiburg in Istanbul on May 20.
Emery spoke to TNT Sports with pride and purpose, pointing first to the supporters whose atmosphere he said was central to the performance.
"It was a special day. The supporters understood it and created an amazing atmosphere. They were playing with us, transmitting their energy, their wishes — and to win this competition is very important with your wishes and desires to show it. During the process, we are doing it. The players responded fantastic on the field."
He identified the specific improvements Villa made after losing the first leg to Forest.
"We were improving things in this match — we needed to improve things, especially some duels which we weren't performing well in. In some moments when we were dominating we needed to be more ruthless, more clinical. We worked after the first leg to improve, and we did it."
His satisfaction with the collective performance was clear.
"I'm so, so proud of how we played the match. The players and the supporters were responding."
He addressed the final directly, setting the tone for how Villa will approach Istanbul.
"It's something special to play a final in Istanbul and we can feel proud of how we achieved it. Now enjoy it, enjoy the process, enjoy the final, enjoy preparing the game, respecting the competition, respecting the final, respecting Freiburg."
Emery placed the achievement in the context of an ongoing process rather than a sudden arrival.
"It makes sense — everything in the process we are in. We are working and sometimes struggling to get in the final like we are playing in two weeks."
This will be Emery's sixth Europa League final, having won the competition three times with Sevilla and reached the final once with Arsenal. Villa face a Freiburg side that eliminated Celta Vigo in the other semi-final.
The Spaniard has done this before. Delivering it for Aston Villa — and their supporters — would be something different entirely.