Espanyol beat Milan and Internazionale to reach the final 19 years ago and - despite racing into a 3-0 lead of what was then a two-legged tie - lost the return match by the same scoreline and went out on penalties.
"For Espanyol the UEFA Cup is a special competition and the players were really determined to get to this final," said Valverde, who actually played in the first leg of that fateful tie. "Having the experience of losing that final has meant that the UEFA Cup has always been a competition close to the hearts of the fans and that makes Wednesday's match doubly special for us.
"It isn't going to be the same though this time as this final is a one-off. We became favourites overnight after the first leg last time, but we didn't know how to manage a situation.
"This time it will be different as we aren't going into the final game with a 3-0 advantage, tomorrow we start at 0-0."
Valverde, 43, took the reins at Espanyol after Miguel Angel Lotina left in the summer despite winning the Copa del Rey as the club had been embroiled in a relegation battle all season. But despite leading them to mid-table security this season, Sevilla are still the firm favourites as they have progressed to a title-challenging side under a former Espanyol boss, Juande Ramos.
"It is understandable that they are seen as the favourites," he admitted. "They are the holders and they have had a brilliant season and still have a chance of winning three trophies, but in a final everyone starts with the same chance.
"What I am more worried about is the intensity and rhythm with which they play football, their self-belief and their speed in attack."