When -- "When" is an conjunction/adverb that means "when", "as when", "at the time when," and "sometimes."

I -- This is from the first-person, singular form of the verb.

sent -- The "I sent" here is a word that means "to send off" and "dispatch." It is the source of our word "apostle."

you -- The "you" here is the second-person, plural pronoun in the form of an object.  

missing "off"  -- (MW) The untranslated word  "off" is from the prefix of the verb. 

without -- "Without" is a proposition which means " without" and "apart from." It is used uniquely by Jesus. He uses a different word that is translated as "without" in two other verses, but the concept of being "without" was one that he seldom used. This is interesting.

purse-- The Greek word translated as "purse" here means "bag", "pouch", and "purse." This word is only used in Luke 10:4.  It doesn't mean a money purse specifically, but any kind of bag. Though Matthew 10:9 has the word "purse" in English translation, the Greek word in that verb means "belt", which is where money was put during the era.

missing "and "  -- (MW) The untranslated word   "and" is used as the conjunction "and", but it also is used to add emphasis ("also"). In English, we would probably used the word "nor" with the negative "without", the Greeks uses the positive conjunction here.

bag -- "Bag" is translated from a Greek word specifically meaning a leather pouch to carry food or provisions for traveling. We might call this a knapsack or provisions bag.

and -- The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

sandals -- "Sandals" is the Greek word for sandals that a person ties on.

did -- This helping verb is used to create questions, commands, negative statements, and smooth word flow in English.

you -- This is from the second-person, plural form of the verb.

missing "no"  -- (MW) The untranslated word   Here, an untranslated negative appears. It is the Greek negative of a subjective opinion, commands, and requests. The sense is that "you don't want" to do or think something. If it wasn't done or wasn't true, the objective negative of fact would be used. However, it does not negate the verb. Here, it comes before the word translated as "anything", which creates the sense "none of this", a phrase the reiterates the idea of not having anything. The "anything" is not the object of the verb, as translated, but a part of this negative phrase.

lack -- The verb translated as "lack" means "to be or to fall behind",  "to fail," and "to be wanting." It is also an uncommon word. But it specifically means "to fail to obtain", which seems to fit here the best.

 anything? -- The Greek word translated as "anything" in the singular means "anyone", "someone," and "anything."  Jesus often uses it to start a question so it means "who", "what", or even "why". Here, it is not the object of the verb as translated, but it modifies a negative that is not translated. The form is "of anything" or "of that". It comes after the untranslated negative.