"Whoever says Real Madrid are dead is always proved wrong in the long term".
Madrid remain in second position, level on points with rivals Barcelona, who will be travelling to Valencia on Sunday.
Lopetegui was notoriously sacked as Spain coach on the eve of the World Cup due to the circumstances in which he joined Real but he said losing a second job this year was not on his mind.
"We don't analyse what people might think", he told reporters when asked about the press reports regarding his uncertain future.
"Sometimes things go your way and other times they don't, the important thing is that the players stick together and we will start scoring again".
Embattled Real boss Lopetegui made five changes to the team that limped to defeat in Moscow, recalling Sergio Ramos and Gareth Bale while leaving out Marco Asensio. "All negative factors are piling up on us", added Lopetegui.
After the global break, Madrid will aim to end their barren run in a home game against Levante on October 20.
Los Blancos dominated the possession for most of the first half, but they were finding it tough to break down the Alaves defence.
Real were left stunned with the final kick of the game as Manu Garcia bundled the ball home from close range to send the home fans into a frenzy.
"This victory takes us to 14 points and that's something tremendous, and it's magnified by the size of the team we have beaten".