"We want to eat a little bit of pulla."
Translation:Me haluamme syödä vähän pullaa.
It's wrong because you used nominative case for "pieni pala". The fact that "pieni pala" is the total object (as opposed to a partial object) of a telic action (an action that can and will reach a state of completion) means that accusative case is required, so it should be "pienen palan". The "pulla" remains a partial object for an obvious reason so it can be kept in partitive case.