After taking a 2-0 lead into the second leg at the Mestalla, Sevilla saw their lead vanish inside 26 minutes, before Jeremy Mathieu's 70th-minute goal had Valencia on track for the European decider.
However, a late intervention from Stephane M'Bia ensured Sevilla of a dramatic progression, as they advanced on away goals after the tie was level 3-3.
Emery was savouring the moment, and was looking no further than celebrating Sevilla's achievement of reaching their third final in the competition since 2005-06.
"Going through like this is unique," Emery said.
"Today our heart was the only thing that got us through the difficulties we had in this match.
"The way I celebrated the goal was natural, that's how it came out.
"I don't care about who we play in the final. We just need to enjoy the occasion. It will be a very beautiful match."
Emery paid tribute to Valencia's comeback, after Juan Antonio Pizzi's men wiped away their deficit in the first half, before standing just seconds from a final berth.
"I wish Valencia lots of luck from here moving forward. They did very well and really participated in the match," Emery said.
"I can't put myself in the position of the Valencia players. Explaining what happened is very difficult.
"We first entered this competition on August 1. We have lived for it and we have shown it so much enthusiasm."
Emery also credited his support crew, claiming M'Bia's winner - assisted by a flick on header from central defender Federico Fazio - was constructed by the off-field tacticians.
"I am happy for my technical staff because they work hard and it was because of their work on the fine details that Fazio was able to win that final header," he said.
