Javi Guerra struck as Valencia won 1-0 at the Mestalla, backing up Saturday's win at Real Madrid.
A delighted Corberan said: “I think that with the numbers and the games the team have won, the objective hasn't yet been achieved. That speaks to the great effort this squad is making, that they have had to make, and will continue to make, to achieve what we all want.
"If with those numbers the objective hasn't yet been achieved, imagine the situation they've experienced and the reaction they've had. I'm pleased to see that the work, commitment, and intensity they put into it is yielding results.
“When you suffer a lot, you really appreciate what you've achieved and what we still have to do to continue achieving. I'm a coach who always takes things one game at a time. Right now, it's time for the players to enjoy today's victory, and so should the fans.
"We're aware of how much the fans have suffered, and they deserve to identify with our performance and see a team giving everything they have to win matches. And starting with the next training session, it'll be time to think about the next match. We haven't achieved our objective yet, and we have to keep fighting hard.”
On the home support, Corberan admits he was "moved" by the atmosphere.
He continued: "I work every day, giving my best to give the fans the best, which I believe is what they deserve. Our goal is for the fans to feel proud of what they see from the team and for us to give them as many wins as possible, since the purpose of my job is to make them proud.
"Then, as for the way to express it, I accept all forms of doing that and focus on continuing to give my best. It fills me with joy that the more than 46,000 people in the stadium are leaving here happy. But not just the fans in the stadium, which is crazy, but also everyone behind it. For those people to go to bed today identifying with the team, happy and joyful, for me that's the best thing.”
Corberan added: “It's impossible not to be moved by Mestalla. It's a privilege to see how people give their all for every ball, and in life, all privileges come with sacrifices, and ours is to continue giving our all to continue creating many of those moments that are thrilling for the coaching staff, the players, and the fans in general who want the best for Valencia CF.”