Zinedine Zidane's men were stunningly beaten 1-0 at the Santiago Bernabeu on Wednesday as Antonio Sanabria headed in a dramatic late winner for the visitors.
The result left Madrid seven points adrift of rivals and league leaders Barcelona, who have won their opening five games.
But Casemiro said his side needed to keep their cool after being left with work to do early in the season.
"We have to have a cool head because maybe a point would be better than a defeat," he said.
"It was bad luck. Everything we created, everything we tried, we fought. It's football. Sometimes it's unfair.
"We have to congratulate Betis, who fought, worked and made a good game here."
Madrid had numerous opportunities as Cristiano Ronaldo made his league return, but the Portuguese star was left frustrated.
Asked about Barca's lead at the top, Casemiro said: "We have to think about ourselves."
Madrid get a chance to bounce back when they visit Deportivo Alaves on Saturday.