The Spanish champions are now seven points off league leaders Barcelona after just five games of the new campaign, but Casemiro has insisted that Real are "the same team that won everything last season".
"It was bad luck, given how much we created, tried and fought. That's football, and sometimes it's unfair. We have to congratulate Betis, who fought, worked hard and had a good game here," Casemiro told reporters.
"We played here in the Champions League here and won. We created several chances, but that's football. There are days when the ball doesn't go in. We have to keep fighting, there's a lot of time left.
"We have seven points to make up, but we have to keep a cool head. We're working hard. We're the same team that won everything last season, and we'll keep working like we have."
Real will look to return to winning ways when they travel to Alaves on Saturday afternoon.