Sofiane Feghouli's opener, Beto's own goal forced from a Jonas header and Jeremy Mathieu's effort seemed to have put los Che into the final, but on-loan QPR midfielder Stephane Mbia nodded home in the 94th minute to silence Mestalla and secure shock progress for Sevilla.
The visitors were outplayed for most of the match but ex-Valencia boss Emery was overjoyed that his players kept believing throughout, comparing the crucial goal to that of Iniesta in the Champions League semi-final at Stamford Bridge five years ago which sent Pep Guardiola's side into the final.
"This is unique," he told Cuatro . "Valencia started well and it was so difficult. Our goal reminded me of Iniesta's goal at Stamford Bridge.
"Today our belief 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're playing in the final, we just need to enjoy the occasion. It will be a very beautiful match.
"I wish Valencia lots of luck from here moving forward. They did very well and really participated in the match. 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."
On-loan midfielder Mbia, who scored in both legs of the semi-final, acknowledged that Valencia made it extremely tough for the visitors and dedicated his goal to his parents.
"It was very difficult for us," the Cameroonian said. "We knew it would be difficult here. That goal was amazing, though.
"I dedicate it to my family, my father and my mother because their lives have been very difficult."