Magic does drain stamina in some instances.
Encountering a Dementor -- which is a dark magical being -- causes horrible feelings and the loss of hope and happiness. It requires chocolate to shake the cold and depression. Is chocolate mana? Sure, why not? :D
Horcruxes cause gloom and doom for a person when they have too much contact with one. Note that Harry, Ron, and Hermione had to take turns wearing the locket so those who weren't wearing it could recuperate from its effects.
We're not sure what Madam Pomfrey gave to Hermione while she was in the hospital wing when she turned into a cat following the Polyjuice Potion incident in Chamber of Secrets, but she was in hospital for about two months, recuperating, and Madam Pomfrey was giving her some kind of medicine to help with the recovery process.
In Goblet of Fire, Harry became exhausted after practicing the Accio summoning charm over and over again, prior to the first task of the Triwizard Tournament.
In Goblet of Fire, Harry was very drained of energy during Priori Incantatem and was barely able to hold onto his wand because the magic was so powerful.
Dumbledore was almost completely drained of his energy following his and Harry's visit to the sea cave, where they retrieved the fake locket Horcrux, and we know he ultimately went on that night to be disarmed by Draco (because he didn't have enough energy to both block Draco's disarming charm and cast Petrificus Totalus on Harry, so he chose to protect Harry and lost his wand accordingly)
These are just some examples.
So, yes, magic can drain energy and stamina, and in some instances a certain food is required to recover from the effects of magic (Dementor/Chocolate)