"No, we do not eat pizza with sausage."
Translation:Ні, ми не їмо піцу з ковбасою.
Accusative is the case for the direct object of the action. Which is, the object most directly affected by the action and changing its state or position the most as the result. Depending on the language different verbs might render same actions differently.
Fortunately, actions like "to eat something", "to make something", "to drink something", "to want something", "to say something", "to read something", "to bring something", "to watch something" and "to listen to something" are rather straightforward in this regard, i.e. "something" is the direct object of such actions (note how on "listen to" English disagrees with me—it requires "to" here). In Ukrainian these go with the Accusative object. Such verbs are called "transitive", if you are into linguistics.
The important thing to understand that verbs used with certain noun "roles" are just a convention inside a language. "To eat" will, probably, be used with Accusative in the vast majority of the languages that have Accusative, but this is not a guarantee. The farther you go into the territory of abstract verbs, the less ground you have to believe that a verb describing a certain action will behave similar across languages.