Carvajal as of now is out for a month, and the team has other right backs. Real Madrid is starting a long stretch without a win, but they are an elite team and should be able to turn it around. Even their keeper, Casilla, is confident they can get back on track. They'll miss Carvajal but they should be ok.
There are other players in the team that are good in playing soccer and they could manage to win. Even though Carvajal is really good the rest of the team is capable to win without him. One man can't do all the work which means that Real Madrid should not worry.
Whether it was likely Real Madrid might have been won most of its matches with Carvajal uninjured, relying on one player to graphically or statistically dominate during play for frequent extended periods of time is an unreliable method for winning a match or several of them through out the season. Instead, this team probably has a combination of competitive individuals equally feted and placed for practicing rhetorically relevant winning successes on the field and positively impacting the outcome of played events, minimally influencing the season for themselves against a limited number of teams or comprehensively in a larger market as well.
It takes an entire group to make up a team. Just because one man is out, that doesn't mean the team is doomed without him. Sure, he may be a large part of the team's success, but there is a good chance that the rest of the team can go on and fill his void.
Carvajal is too key of a player for Real Madrid to have much of a chance without him. His ball handling skills are far beyond the rest of his teammates. He also makes the most of what he has, because he is a smart player. He gets the best out of his teammates and they will miss him.