The Wales international has come in for criticism already this season following a slow start by Los Blancos, culminating in a second successive home league draw last weekend.
Bale was guilty of missing a couple of chances in that match and was also jeered at times during Madrid's 3-0 win over APOEL in the Champions League on Wednesday night.
Casemiro has backed the former Tottenham Hotspur man to prove his critics wrong, however, while also heaping praise on Cristiano Ronaldo following the Portuguese forward's brace on his return to action against the Cypriot champions.
"You can see that Bale is working, he wants to score goals and he's fighting to always help Real Madrid," he told reporters. "Speaking of Cristiano is also very easy, we know that he's the best in the world. We're happy having him back and he looks strong. With his ability we always want to have him available.
"There is no worry in the dressing room. We have drawn two games and people start talking, but we are calm and we are working just the same. This is football. There are days when you draw, there are days when things don't go well.
"But we have achieved three important points for us [against APOEL], especially to gain confidence ahead of a difficult match we have against Real Sociedad on Sunday."