That the Cardinals were even in the position to win was historic in itself as it marked the second biggest September deficit overcome in major league history and the largest in National League history. Only the Tampa Bay Rays, who overcame a nine-game deficit this year, have overcome a larger one.
However the Rays lost their series against the Texas Rangers. That means that the Cardinals have now overcome the largest deficit to make it to the NLCS.
A couple of other tidbits on this note. First, there is the irony that the Phillies swept the Atlanta Braves to end the season. Without that sweep, they would not have had to face the Cardinals.
The other is that the Cardinals have twice before overcome large September deficits to make it to the postseason. In 1964 they trailed by 7.5 games and went on to win the World Series. The team they trailed, and swept in the second to last series of the season to get to the World Series (there were no playoffs yet) was the Philadelphia Phillies. There, they beat the New York Yankees.
In 1934 on September 1 they trailed by 5.5 games and by 7.5 games on September 5. They again went on to win the World Series where they beat the Detroit Tigers.