First of all, you're lifting up the WHOLE packet, whereas you only need to 'break' the packet with your thumb.
A 'thumb break' would be the proper terminology.
Once you make the thumb break, the bottom packet should fall into your hand so you kind of have this '<' going on.
Tilt your hand downwards a little bit and towards the left (if you're doing it with the right. Down and to the right if you're doing it with the left). The ONLY finger that should have any contact with the bottom packet should be the pinky to prevent it from dropping into oblivion. The top packet should only be held up by the thumb, middle and ring fingers. The pointer finger is free-up at this point.
Now, you can use your pointer to go back behind the bottom packet (preferably as middle as you can) and push it up and towards you, so the only thing holding it up now is the pointer and thumb.
This should cause the top packet to drop once this happens after you go as far as you can with the bottom packet.
Once the top packet drops, it should now be the bottom packet.
All that should be done is to release your pointer finger. Tilt your hand upwards (parallel with the ground), and downwards (using your wrist as an unmoving pivot point, but moving the rest of your hand downwards so that the packet gently falls on the the rest of the deck).
I will say this, I wrote this very early in the morning. If something doesn't make sense, I encourage engine to correct me in this or to ask for clarification.