Hugo Duro had Valencia ahead before Real struck twice in the final minutes to win 2-1, despite the dismissal of Vini Jr.
Corberan, on debut, said afterwards: "The feeling of defeat is like one of mourning. The atmosphere was extraordinary and the team at times played the football that we have been working on. I'm happy with the commitment and dedication of the team, but if you don't win, we are aware that you have to improve.
"We have only been working together for a few days, and we have greatly reinforced the team's commitment to what we want to build together. We were impressed by the support of the fans who make Mestalla a very difficult ground for opponents
"My focus is on the process that we have started to work on with the players. As a coach, for me the results have to be a consequence of our performance on the pitch. There have been moments from the team that I liked, and others that we have to continue working on. In my mind there is only that: Improving my team.
"The team had good moments, I think we showed a personality and character that it was important for us to show. Real Madrid had just won a world title and we know the power of that team, and in the match there were moments in which we were unable to impose the game that I am convinced that -if we work hard- we will gradually achieve by imposing ourselves."