Well, Some people might say that Real Madrid does have some young talents in tone of benches but these players will not be as effective as the first team. It also brings lots of pressure that force the club to look for possible short terms solutions, particularly in high profile matches such as El Clásico against Barcelona. A defeat such as this would most definitely put pressure in the team and maybe make the management push for players in the upcoming January transfer window in case the require them.
Indeed, even though Real Madrid has substitute players, but still, to face El Classico, they must have a much stronger defense. And indeed the problem is that Carvajal is one of Real Madrid's mainstay defenders. The most likely substitute is Vazquez who is trusted by Ancelotti for the intermediate replace Carvajal Position.
Source: replace Carvajal - Vazquez
Luckily, I read the news that some of their players will return from their injuries in El Classico later, such as Courtois and Miliato who are scheduled to be ready on October 10th. So, at least this is much better than the current condition.