Only a Jew draws G-dliness through a Mitzvah:
Mitzvos are compared to wood. Just as wood fuels a fire, so too Mitzvos fuel the Shechina. It is for this precise reason that the Mitzvos must be performed by a Jew for them to be effective, as only a Jew contains the inner Bittul/nullification necessary to allow the Mitzvah, the log, to burn. One who has Yeishus/ego and does a Mitzvah is comparable to a log that is stiff and does not catch fire. The Bittul found in a Jew is his ability to give up his life for the sake of Hashem. Performing Mitzvos with the inner power of Bittul is similar to the relationship between a seed and the earth. A seed will only grow when planted in earth. Place a seed on the table and it will not sprout anything. The same applies with Mitzvos; place a pair of Tefillin on the table or on a gentile and it has no effect, and brings no revelation of G-dliness to any area. When a Jew however wears the Tefillin it draws down revelation of G-dliness. Specifically, the Jewish people are referred to as Eretz Heifetz, the land that G-d desired, and contains fertile soil to sprout the Mitzvos they perform.
 Likkutei Torah Acharei Mos 27a
 Torah or Shemos 53c