If you have a Cape, you can use this to fly above the top of the stage and into the area above the narrow hallway.
The Secret Exit is through a different door. The 2nd door you come across while you're about the hallway, so it should be after the door that leads to the normal exit.
You'll get a 3-UP moon if you went through the right door.
![](https://i.ytimg.com/vi/shhSS02PUik/mqdefault.jpg)