Verb phrases can be simple, as in a main verb plus its helping verb, or complex, including adverbs, direct objects and indirect objects. Because a verb phrase comprises the verb itself plus other elements of the predicate, a direct object is by definition part of the verb phrase.
A direct object is the noun or pronoun that carries the action of the verb. In the sentence, “Zeke saw a wombat,” the direct object is “wombat”; it is what the subject, Zeke, saw. The verb phrase in this sentence is “saw a wombat,” the verb itself, the direct object (noun) and the article, “a.”
Some verbs in English are inherently two-part constructions; these idioms include a second word, called a participle, which completes the meaning of the verb. These phrasal verbs can take direct objects, and the whole construction then becomes a verb phrase in the general sense. An example is “pick up,” which has a different meaning as a verb than simply “pick.” For example, “Zeke picked up the wombat.” “Wombat” is still the direct object, what he picked up. “Picked up” is the two-word phrasal verb, and the whole predicate is the verb phrase “picked up the wombat.”