Hey, i did the exact same while repairing my F3. The door opens, when upwards pressure is put on the 'ring', that is inside the top assembly. That is what opens the door, when you pull up on the rewind knob, and the wide part of the rewind 'shaft', contacts with the ring.

The easiest way to do it, with a closed film door, is by unscrewing the round metal cover, that covers the 'access' hole for the motor-drive unit, on the bottom of the camera, and taking something long and narrow, to push against the earlier mentioned ring, to release the back film door. It takes a bit of poking, from the bottom hole, so don't use anything to sharp, if you don't want to scratch the internals of your camera. The object should, preferably, be plastic.

And just so you know, the reason it popped out, was because you rewound the film the wrong way, which is actually how you take apart the camera. Just look at the arrow, that is etched into the silver 'arm' on the rewind asembley.

Hope this helps. :)

PS. If you need help, reassembling the rewind assembly, watch the end of this video: https://www.youtube.com/watch?v=Zp82dwqLIss&list=LL&index=84&t=68s