Valencia triumphed 5-3 on aggregate to reach the Europa League semi-finals after overturning a 3-0 first-leg deficit, with Alcacer, Eduardo Vargas and Juan Bernat sealing the astounding comeback after extra time.
"As long as I live, I'll never forget this hat-trick," Alcacer said after the match.
"It's been my first in front of the Valencia fans. I'm very happy and I dedicate it to my team-mates, because without them, I couldn't have scored."
The 20-year-old dedicated the win to Valencia's fans, while he also paid tribute to Oscar Martinez, a local young footballer, who recently died of a heart attack.
"The fans have been with us right to the end. These fans are always there, through the good and the bad," he added.
"We would like to dedicate this win to them and most of all, Oscar Martinez, the youngster from Ontinyent, who is always in our minds."
Valencia head into Friday's draw for the semi-finals along with Juventus, Benfica and fellow Liga side Sevilla.