Madrid have endured a tough campaign and look set to only have the Club World Cup to show for it after the failures of Julen Lopetegui and Santiago Solari in the Santiago Bernabeu hot seat.
Los Blancos won three consecutive Champions League titles in Zinedine Zidane's first stint at the helm but failed to recreate that dominant form this season, suffering a last-16 elimination against Ajax.
Madrid were dealt their first loss since Zidane's return on Wednesday as Karim Benzema's late header proved a mere consolation after goals from Goncalo Guedes and Ezequiel Garay at Mestalla.
"I don't believe Valencia were the better team. I think we controlled the first half," he said post-match. "Then they scored in the last 10 minutes.
"We'd had the game in our hands and then, with the goal, of course they got on top, the fans played their part.
"In the second half, we tried and we worked hard. But football is about goals. They got to 2-0, we kept working, kept trying and made it 2-1 late on.
"The defeat is tough, but we are thinking about our hard work. We have to go game by game. We know we are not at our best, but we have got to keep working.
"When you lose, you all lose. When I say we're not right, that goes for all of us. We're trying, we're working.
"We were playing against a great team, a team that is tough to come here and play against. It's a difficult game, but we had the game in our hands."
However, Casemiro conceded there was no excuse for Madrid's results, despite their endeavour.
"Real Madrid have to be at their best in every single training session and every single game," he said. "We have to improve.
"We have a game at home against Eibar [on Saturday] - we've got to think about that game. We know it's a tough moment, but we count on the fans.
"We know it's not easy for us right now, but we're working hard to come back next year. Madrid always come back."