Lopetegui was sacked after their Champions League defeat to Borussia Dortmund. He is expected to be replaced by Jorge Sampaoli.
He said after the loss: "My feelings are complicated, mixed. The first thing that comes into my head, and my heart, is gratitude – gratitude to my club, to the city, to the Sevilla supporters, to the players, to everyone who works for Sevilla, Monchi, everybody. We've experienced some wonderful things. Also sadness – I'm sorry to leave a club that I love and that I'm convinced will go forward.
"Often what you take from the places where you've been is the affection and recognition of what you've done. This is something that fills me with pride and makes me happy in this sad situation. The Sevilla fans are very demanding, and this is one of the big assets of this club. It means everyone has given their best."
Lopetegui was given a standing ovation by the Sevilla support at the final whistle.
"I insist that Sevilla will carry on without Julen Lopetegui ... The demanding nature of Sevilla and their fans will never be lost – I think it's what really makes this club keep the competitive tension that has kept them so high. I'm sure this group of players, as soon as they adjust two or three things, will achieve important results again.
"We managed to create a unique history in the story of a club as big as Sevilla and people recognise that … the recognition from the public at the end I will carry in my heart forever. Nobody can take that away from me."