Nuno left his role as Valencia coach after his side lost 1-0 to Sevilla and were reduced to nine men.
Sevilla, who lost 4-2 to Borussia Monchengladbach in the Champions League in midweek, should have had more to show for their dominance than Sergio Escudero's second-half volley as the visitors had Joao Cancelo and Javi Fuego sent off.
And Nuno revealed his departure in his post-game press conference, saying: "It has been an honour to coach Valencia."
Sevilla were on the front foot throughout but had to wait until the 31st minute before forcing Valencia goalkeeper Maty Ryan into his first save when the Australian turned away Fernando Llorente's header from impressive Ukrainian Yevhen Konoplyanka's cross.
Valencia were reduced to 10 men in the 35th minute when right-back Joao Cancelo received a second yellow card for raising an arm and the visitors survived another scare just before the break when Konoplyanka's goalbound strike was blocked by Aderllan Santos.
Sevilla deservedly made the breakthrough in the 50th minute when Argentinian midfielder Ever Banega's brilliant pass with the outside of his foot was volleyed home first time by Escudero.
Mariano's shot from inside the area was saved by Ryan, who comfortably dealt with Konoplyanka's header as Sevilla chased a second goal.
Sevilla's former Blackburn and Stoke midfielder Steven Nzonzi crashed a half-volley just over the crossbar and Adil Rami's goalbound header was deflected over by Santos before Javi Fuego's late challenge in the 78th minute earned the Valencia midfielder a second yellow card.
Valencia poured men forward in the closing stages in the hope of salvaging a point but it was in vain - and their 11-year wait for victory at Sevilla will continue under a new coach.
Nuno said in comments reported by Marca: "The situation is not good and I'm an employee of the club.
"It has been an honour to coach Valencia. I want to thank all the players for their efforts and thank (owner) Peter Lim and the fans of a great club.
"We have the youngest squad in the league and it is important Valencia follow through and believe in this project.
"On Monday there will be a meeting to clarify the future."