In films and fiction books they always just shove something in their tunic and it magically stays there until they need it. It seems unlikely. How did people store personal belongings on them?
The short answer is no, no pockets.
The long answer is that you wouldn't generally speaking have pockets built into your clothing like we do, but you might have a pouch, purse or scrip which fastened to your belt or girdle. A drawstring design like this done on linen would be a good guide for a woman's alms-purse - it dates to the mid-1300s in France - though this is of course an unusually ornate and costly example, given just how much gold and silver thread is involved! Samite might also be an option, but only for the VERY wealthy.
You see how it has the drawstring across the mouth of the bag (disregard the tassels, they're decorative), and then the two loops of thread? The bag would be tied or hooked on at about hip height, next to a ring of keys, her personal knife for mealtimes or any other personal items the owner wished to keep convenient.
Bags for men might be of a similar drawstring type (this was common for both men and women) or might be a more sturdy leather scrip.