The simple answer is quite simply to search for the app you are looking for using Facebook’s search bar.
According to Facebook (see quote below), the reason the Facebook app directory is gone is because no one ever really used it.
Product manager Carl Sjogreen posted on the Facebook Developers Blog:
Many developers have been confused about what it means to submit to the app directory and frustrated by the length of time it took to get approved. As we have looked into this issue, we found that the app directory drove less than 0.5 percent of all app installs, while a significant number of app installs came as a result of Facebook search. Until now, to be visible in search, you had to submit your app to the app directory.
Today, we are announcing two updates to decouple the search submission from the directory to make it easier for you to get your app into the Facebook search index:
We are removing the app directory (in its current form) since it does not drive a significant amount of traffic to your apps.
We are creating a new, simplified way to get your app into the Facebook search index.
For your app to show up in search (if it’s not already listed and has over 10 monthly active users), simply go to the developer app and click the “submit to search” link in the left sidebar when editing your app.
After clicking the link, we will submit your app to our search index. There is no longer an approval process for getting your app into search. When you make any changes to your app settings, we will automatically update the listing. It can take up to 72 hours for your app to appear in search results. As always, there is no approval process for launching an app on Platform.
We do not expect any noticeable decrease in traffic to your apps as a result of these changes and continue to focus our energy on social channels that deliver meaningful distribution to your apps.
So you are going to be missing the Facebook app directly?
According to Facebook, more than likely you never used it in the first place.
What are you thoughts about the Facebook app directory being gone?
via AllFacebook