Learn German: Ich habe die Milch nicht vertragen.

When you negate the entire action in the present perfect tense (the Perfekt), nicht moves to the end of the clause, just before the past participle. Here, it sits right before the participle vertragen to show that the action of tolerating didn't happen.

Since milk is a noun, why don't we use keine instead of nicht here?

You use keine to negate nouns that have an indefinite article (like ein) or no article at all. Because we are talking about specific milk using the definite article die, we must use nicht to negate the sentence.

Why does the past participle vertragen lack the usual ge- prefix?

The verb vertragen starts with the inseparable prefix ver-. Verbs with inseparable prefixes (like ver-, be-, ent-) do not take a ge- in their past participle form. They simply keep their standard prefix.

Is vertragen only used for digesting food?

Not at all! While it perfectly translates to stomaching food or medicine, you can also use it for tolerating loud noises, heat, or even getting along with people (when used reflexively, as in sich vertragen).