You can not pick up mushrooms. If you stand beside mushrooms, certain plants, rotten food, etc, you can drag and drop an empty flask (or stack of flasks; only one will get used) onto it to create a potion. Level 1 of Alchemy allows you to mix potions, while level 2 lets you create minor potions (see the alchemy topic link above).
KillingMoon, the mushroom shouldn't have disappeared if you didn't have a high enough level to create a potion. The flask should have gone back into your inventory.
